메뉴 건너뛰기




Volumn , Issue , 2008, Pages 1-328

Nonlinear Dynamics of Piecewise Constant Systems and Implementation of Piecewise Constant Arguments

Author keywords

[No Author keywords available]

Indexed keywords


EID: 73249141287     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/6882     Document Type: Book
Times cited : (97)

References (190)
  • 1
    • 0000327582 scopus 로고
    • Oscillatory and Periodic Solutions for Systems of Two First Order Linear Differential Equations with Piecewise Constant Argument
    • Aftabizadeh, A. R. and Wiener, J., “Oscillatory and Periodic Solutions for Systems of Two First Order Linear Differential Equations with Piecewise Constant Argument,” Applicable Analysis, Vol. 26, pp. 327-338, 1988.
    • (1988) Applicable Analysis , vol.26 , pp. 327-338
    • Aftabizadeh, A.R.1    Wiener, J.2
  • 2
    • 0000153927 scopus 로고
    • Models of Vertically Transmitted Disease with Sequential Continuous Dynamics
    • (V. Lakshmikantham, Ed.), Academic Press, New York
    • Busenberg, S. and Cooke, K. L., Models of Vertically Transmitted Disease with Sequential Continuous Dynamics, in “Nonlinear Phenomena in Mathematical Sciences” (V. Lakshmikantham, Ed.), Academic Press, New York, pp. 179-189, 1982.
    • (1982) Nonlinear Phenomena in Mathematical Sciences , pp. 179-189
    • Busenberg, S.1    Cooke, K.L.2
  • 5
    • 0008402812 scopus 로고
    • Retarded Differential Equations with Piecewise Constant Delays
    • Cooke, K. L. and Wiener, J., “Retarded Differential Equations with Piecewise Constant Delays,” Journal of Mathematical Analysis and Applications, Vol. 99, No. 1, pp. 256-297, 1984.
    • (1984) Journal of Mathematical Analysis and Applications , vol.99 , Issue.1 , pp. 256-297
    • Cooke, K.L.1    Wiener, J.2
  • 7
    • 0028761203 scopus 로고
    • On Oscillatory Motion of Spring-Mass Systems Subjected to Piecewise Constant Forces
    • Dai, L. and Singh, M. C., “On Oscillatory Motion of Spring-Mass Systems Subjected to Piecewise Constant Forces,” Journal of Sound and Vibration, Vol. 173, pp. 217-233, 1994.
    • (1994) Journal of Sound and Vibration , vol.173 , pp. 217-233
    • Dai, L.1    Singh, M.C.2
  • 8
    • 0001391381 scopus 로고    scopus 로고
    • Periodic, Quasiperiodic and Chaotic Behavior of a Driven Froude Pendulum
    • Dai, L. and Singh, M. C., “Periodic, Quasiperiodic and Chaotic Behavior of a Driven Froude Pendulum,” International Journal of Non-Linear Mechanics, Vol. 33, No. 6, pp. 947-965, 1998.
    • (1998) International Journal of Non-Linear Mechanics , vol.33 , Issue.6 , pp. 947-965
    • Dai, L.1    Singh, M.C.2
  • 9
    • 0037809833 scopus 로고    scopus 로고
    • A New Approach to Approximate and Numerical Solutions of Oscillatory Problems
    • Dai, L. and Singh, M. C., “A New Approach to Approximate and Numerical Solutions of Oscillatory Problems,” Journal of Sound and Vibration, Vol. 263, No. 3, pp. 535-548, 2003.
    • (2003) Journal of Sound and Vibration , vol.263 , Issue.3 , pp. 535-548
    • Dai, L.1    Singh, M.C.2
  • 10
    • 34248356734 scopus 로고    scopus 로고
    • A Study on the Effects of Workpiece Deflection and Motor Features on Nonlinear Vibrations in Machining
    • Dai, L. and Wang, J. “A Study on the Effects of Workpiece Deflection and Motor Features on Nonlinear Vibrations in Machining,” Journal of Vibration and Control, Vol. 13, No. 5, pp. 557-582, 2007.
    • (2007) Journal of Vibration and Control , vol.13 , Issue.5 , pp. 557-582
    • Dai, L.1    Wang, J.2
  • 12
    • 29544435349 scopus 로고    scopus 로고
    • Periodic Solutions and Oscillation of Discrete Nonlinear Delay Population Dynamics Model with External Force
    • Elabbasy, E. M. and Saker, S. H., “Periodic Solutions and Oscillation of Discrete Nonlinear Delay Population Dynamics Model with External Force,” IMA Journal of Applied Mathematics, pp. 1-15, 2005.
    • (2005) IMA Journal of Applied Mathematics , pp. 1-15
    • Elabbasy, E.M.1    Saker, S.H.2
  • 13
    • 0017913041 scopus 로고
    • Seasonal Dynamics of American Dog Tick, Dermacentor Variabilis (say), Population in South Western Nova Scotia
    • Garvie, M. B., McKiel, J. A., Sonenshine, D. E., and Campbell, A., “Seasonal Dynamics of American Dog Tick, Dermacentor Variabilis (say), Population in South Western Nova Scotia,” Canadian Journal of Zoology, Vol. 65, pp. 28-39, 1978.
    • (1978) Canadian Journal of Zoology , vol.65 , pp. 28-39
    • Garvie, M.B.1    McKiel, J.A.2    Sonenshine, D.E.3    Campbell, A.4
  • 14
    • 2642587972 scopus 로고    scopus 로고
    • Periodic Solutions of a Discrete Time Non-Autonomous Ratio-Dependent Predator–Prey System
    • Fan, M. and Wang, K., “Periodic Solutions of a Discrete Time Non-Autonomous Ratio-Dependent Predator–Prey System,” Mathematical and Computer Modelling, Vol. 35, pp. 951–961, 2002.
    • (2002) Mathematical and Computer Modelling , vol.35 , pp. 951-961
    • Fan, M.1    Wang, K.2
  • 15
    • 84880026161 scopus 로고
    • Some Characteristics of Simple Types of Predation and Parasitism
    • Holling, C. S., “Some Characteristics of Simple Types of Predation and Parasitism,” The Canadian Entomologist, Vol. 91, pp. 385–398, 1959.
    • (1959) The Canadian Entomologist , vol.91 , pp. 385-398
    • Holling, C.S.1
  • 16
    • 0002366911 scopus 로고
    • The Functional Response of Predators to Prey Density and Its Role in Mimiery and Population Regulation
    • Holling, C. S., “The Functional Response of Predators to Prey Density and Its Role in Mimiery and Population Regulation,” Memoirs of the Entomological Society of Canada, Vol. 45, pp. 3–60, 1963.
    • (1963) Memoirs of the Entomological Society of Canada , vol.45 , pp. 3-60
    • Holling, C.S.1
  • 17
    • 0025449148 scopus 로고
    • Oscillations and Asymptotic Stability of Solutions of First Order Neutral Differential Equations with Piecewise Constant Argument
    • Huang, Y. K., “Oscillations and Asymptotic Stability of Solutions of First Order Neutral Differential Equations with Piecewise Constant Argument,” Journal of Mathematical Analysis and Applications, Vol. 149, pp. 70-85, 1990.
    • (1990) Journal of Mathematical Analysis and Applications , vol.149 , pp. 70-85
    • Huang, Y.K.1
  • 18
    • 84968519032 scopus 로고
    • Variation of Parameters Formula for the Equation of Cooke and Wiener
    • Jayasree, K. N. and Deo, S. G., “Variation of Parameters Formula for the Equation of Cooke and Wiener,” Proceedings of the American Mathematical Society, Vol. 112, No. 1. pp. 75-80, 1991.
    • (1991) Proceedings of the American Mathematical Society , vol.112 , Issue.1 , pp. 75-80
    • Jayasree, K.N.1    Deo, S.G.2
  • 20
    • 0024281664 scopus 로고
    • Direct Method for the Steady State Response of Structures
    • Leung, A.Y.T., “Direct Method for the Steady State Response of Structures,” Journal of Sound and Vibration, Vol. 124, pp. 135-139, 1988.
    • (1988) Journal of Sound and Vibration , vol.124 , pp. 135-139
    • Leung, A.Y.T.1
  • 21
    • 0008291269 scopus 로고    scopus 로고
    • Global Stability and Chaos in a Population Model with Piecewise Constant Arguments
    • Liu, P. and Gopalsamy, K., “Global Stability and Chaos in a Population Model with Piecewise Constant Arguments,” Applied Mathematics and Computation, Vol. 101, pp. 63-88, 1999.
    • (1999) Applied Mathematics and Computation , vol.101 , pp. 63-88
    • Liu, P.1    Gopalsamy, K.2
  • 23
    • 34250789774 scopus 로고    scopus 로고
    • Existence, Uniqueness and Asymptotic Behavior of the Solutions of a Fuzzy Differential Equation with Piecewise Constant Argument
    • Papaschinopoulos, G., Stefanidou, G., and Efraimidis, P., “Existence, Uniqueness and Asymptotic Behavior of the Solutions of a Fuzzy Differential Equation with Piecewise Constant Argument,” Information Sciences, Vol. 177, pp. 3855-3870, 2007.
    • (2007) Information Sciences , vol.177 , pp. 3855-3870
    • Papaschinopoulos, G.1    Stefanidou, G.2    Efraimidis, P.3
  • 25
    • 0033690907 scopus 로고    scopus 로고
    • Predicting High-Speed Machining Dynamics by Substructure Analysis
    • Schmitz, T. and Donaldson, R., Predicting High-Speed Machining Dynamics by Substructure Analysis, CIRP Annals, Vol. 49, No. 1, pp. 303-308, 2000.
    • (2000) CIRP Annals , vol.49 , Issue.1 , pp. 303-308
    • Schmitz, T.1    Donaldson, R.2
  • 28
    • 33748293096 scopus 로고    scopus 로고
    • Positive Periodic Solutions of Discrete Three-Level Food-Chain Model of Holling Type II
    • Sun, Y. G., Saker, S. H., “Positive Periodic Solutions of Discrete Three-Level Food-Chain Model of Holling Type II,” Applied Mathematics and Computation, Vol. 180, pp. 353-365, 2006.
    • (2006) Applied Mathematics and Computation , vol.180 , pp. 353-365
    • Sun, Y.G.1    Saker, S.H.2
  • 31
    • 33846893200 scopus 로고    scopus 로고
    • Oscillation of a Differential Equation with Fractional Delay and Piecewise Constant Arguments
    • Wang, Y. and Yan, J., “Oscillation of a Differential Equation with Fractional Delay and Piecewise Constant Arguments,” Computers and Mathematics with Applications, Vol. 52, pp. 1099-1106, 2006.
    • (2006) Computers and Mathematics with Applications , vol.52 , pp. 1099-1106
    • Wang, Y.1    Yan, J.2
  • 35
    • 0036497509 scopus 로고    scopus 로고
    • The Existence of Almost Periodic Solutions of Retarded Differential Equations with Piecewise Constant Argument
    • Yuan, R., “The Existence of Almost Periodic Solutions of Retarded Differential Equations with Piecewise Constant Argument,” Nonlinear Analysis, Vol. 48, pp. 1013-1032, 2002.
    • (2002) Nonlinear Analysis , vol.48 , pp. 1013-1032
    • Yuan, R.1
  • 36
    • 0039116174 scopus 로고
    • Oscillatory and Nonoscillatory Properties of First Order Differential Equations with Piecewise Constant Deviating Arguments
    • Zhang, B. G., and Parhi, N. “Oscillatory and Nonoscillatory Properties of First Order Differential Equations with Piecewise Constant Deviating Arguments,” Journal of Mathematical Analysis and Applications, Vol. 139, pp. 23-25, 1989.
    • (1989) Journal of Mathematical Analysis and Applications , vol.139 , pp. 23-25
    • Zhang, B.G.1    Parhi, N.2
  • 38
    • 0018992908 scopus 로고
    • Lyapunov Characteristic Exponents for Smooth Dynamical Systems and for Hamiltonian Systems: A Method for Computing All of Them
    • Bennetin, G., Galgani, L., Giorgilli, A., and Strelcyn, J. M., “Lyapunov Characteristic Exponents for Smooth Dynamical Systems and for Hamiltonian Systems: A Method for Computing All of Them,” Meccanica, Vol. 15, pp. 9-30, 1980.
    • (1980) Meccanica , vol.15 , pp. 9-30
    • Bennetin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.M.4
  • 48
    • 0000327582 scopus 로고
    • Oscillatory and Periodic Solutions for Systems of Two First Order Linear Differential Equations with Piecewise Constant Argument
    • Aftabizadeh, A. R. and Wiener, J., “Oscillatory and Periodic Solutions for Systems of Two First Order Linear Differential Equations with Piecewise Constant Argument,” Applicable Analysis, Vol. 26, pp. 327-338, 1988.
    • (1988) Applicable Analysis , vol.26 , pp. 327-338
    • Aftabizadeh, A.R.1    Wiener, J.2
  • 51
    • 0015602944 scopus 로고
    • An Approximate Solution to a Strongly Non-Linear, Second-Order, Differential Equation
    • Christopher, P. A. T., “An Approximate Solution to a Strongly Non-Linear, Second-Order, Differential Equation,” International Journal of Control, Vol. 17, No. 3, pp. 597-608, 1973.
    • (1973) International Journal of Control , vol.17 , Issue.3 , pp. 597-608
    • Christopher, P.A.T.1
  • 52
    • 0008402812 scopus 로고
    • Retarded Differential Equations with Piecewise Constant Delays
    • Cooke, K. L. and Wiener, J., “Retarded Differential Equations with Piecewise Constant Delays,” Journal of Mathematical Analysis and Applications, Vol. 99, No. 1, pp. 256-297, 1984.
    • (1984) Journal of Mathematical Analysis and Applications , vol.99 , Issue.1 , pp. 256-297
    • Cooke, K.L.1    Wiener, J.2
  • 54
    • 0028761203 scopus 로고
    • On Oscillatory Motion of Spring-Mass Systems Subjected to Piecewise Constant Forces
    • Dai, L. and Singh, M. C., “On Oscillatory Motion of Spring-Mass Systems Subjected to Piecewise Constant Forces,” Journal of Sound and Vibration, Vol. 173, pp. 217-233, 1994.
    • (1994) Journal of Sound and Vibration , vol.173 , pp. 217-233
    • Dai, L.1    Singh, M.C.2
  • 55
    • 85126425135 scopus 로고
    • Recent Developments in Dynamics and Vibration
    • Den Hartog, J. P., “Recent Developments in Dynamics and Vibration,” Applied Mechanics Reviews, Vol. 4, No. 1, pp. 2-3, 1951.
    • (1951) Applied Mechanics Reviews , vol.4 , Issue.1 , pp. 2-3
    • Den Hartog, J.P.1
  • 57
    • 0023577901 scopus 로고
    • Numerical Simulations of Periodic and Chaotic Responses in a Stable Duffings System,”
    • Fang, T. and Dowell, E. H., “Numerical Simulations of Periodic and Chaotic Responses in a Stable Duffing’s System,” International Journal of Nonlinear Mechanics, Vol. 22, No. 5, pp. 401-425, 1987.
    • (1987) International Journal of Nonlinear Mechanics , vol.22 , Issue.5 , pp. 401-425
    • Fang, T.1    Dowell, E.H.2
  • 58
    • 49049134700 scopus 로고
    • Chaotic Attractors of an Infinite-Dimensional Dynamical System
    • Farmer, J. D., “Chaotic Attractors of an Infinite-Dimensional Dynamical System,” Physica, Vol. 40, pp. 366-393, 1982.
    • (1982) Physica , vol.40 , pp. 366-393
    • Farmer, J.D.1
  • 61
    • 85126403177 scopus 로고
    • Mechanical Vibrations: Their Cause and Prevention
    • Inglis, C. E., “Mechanical Vibrations: Their Cause and Prevention,” Institution of Civil Engineers (London), Vol. 22, No. 8, pp. 312-357, 1944.
    • (1944) Institution of Civil Engineers (London) , vol.22 , Issue.8 , pp. 312-357
    • Inglis, C.E.1
  • 62
    • 84968519032 scopus 로고
    • Variation of Parameters Formula for the Equation of Cooke and Wiener
    • Jayasree, K. N. and Deo, S. G., “Variation of Parameters Formula for the Equation of Cooke and Wiener,” Proceedings of the American Mathematical Society, Vol. 112, No. 1. pp. 75-80, 1991.
    • (1991) Proceedings of the American Mathematical Society , vol.112 , Issue.1 , pp. 75-80
    • Jayasree, K.N.1    Deo, S.G.2
  • 64
    • 0006451452 scopus 로고
    • Beitrag zur näherungsweisen Integration totaler Differentialgleichungen
    • Kutta, W., “Beitrag zur näherungsweisen Integration totaler Differentialgleichungen,” Zeitschrift fur Mathematik und Physik, Vol. 46, pp. 435-453, 1901.
    • (1901) Zeitschrift Fur Mathematik Und Physik , vol.46 , pp. 435-453
    • Kutta, W.1
  • 67
    • 38249017901 scopus 로고
    • Chaotic Behavior of Some Piecewise-Linear Systems, Part I: Systems with Set-Up Spring or with Unsymmetric Elasticity
    • Mahfouz, I. A. and Badrakhan, F., “Chaotic Behavior of Some Piecewise-Linear Systems, Part I: Systems with Set-Up Spring or with Unsymmetric Elasticity,” Journal of Sound and Vibration, Vol. 143, pp. 255-288, 1990.
    • (1990) Journal of Sound and Vibration , vol.143 , pp. 255-288
    • Mahfouz, I.A.1    Badrakhan, F.2
  • 68
    • 85003340059 scopus 로고
    • Optimal Predictor-Corrector Method for Systems of Second-order Differential Equations
    • Morino, L., Leech, J. W. and Witmer, E. A., “Optimal Predictor-Corrector Method for Systems of Second-order Differential Equations,” AIAA Journal, Vol. 12, No. 10, pp. 1343-1347, 1974.
    • (1974) AIAA Journal , vol.12 , Issue.10 , pp. 1343-1347
    • Morino, L.1    Leech, J.W.2    Witmer, E.A.3
  • 70
    • 0012650693 scopus 로고
    • Ueber die numerische Auflösung totaler Differential gleichungen
    • Runge, C., “Ueber die numerische Auflösung totaler Differential gleichungen,” Mathematische Annalen, Vol. 46, pp. 167-178, 1895.
    • (1895) Mathematische Annalen , vol.46 , pp. 167-178
    • Runge, C.1
  • 75
    • 0023410905 scopus 로고
    • Characteristics of Numerical Simulations of Chaotic Systems
    • Tongue, B. H., “Characteristics of Numerical Simulations of Chaotic Systems,” Journal of Applied Mechanics, Vol. 54, pp. 695-699, 1987.
    • (1987) Journal of Applied Mechanics , vol.54 , pp. 695-699
    • Tongue, B.H.1
  • 76
    • 0001804640 scopus 로고
    • Steady Motions Exhibited by Duffings Equation: A Picture Book of Regular and Chaotic Motions,”
    • (editor P.J. Holmes), Philadelphia: SIAM
    • Ueda, Y., “Steady Motions Exhibited by Duffing’s Equation: A Picture Book of Regular and Chaotic Motions,” in New Approaches to Nonlinear Problems in Dynamics, (editor P.J. Holmes), Philadelphia: SIAM., pp. 311-322, 1980.
    • (1980) New Approaches to Nonlinear Problems in Dynamics , pp. 311-322
    • Ueda, Y.1
  • 77
    • 0039418688 scopus 로고
    • Explosion of Strange Attractors Exhibited by Duffing’s Equation
    • Helleman, R. H. G. (ed.), New York Academy of Sciences, New York
    • Ueda, Y., Explosion of Strange Attractors Exhibited by Duffing’s Equation, in Nonlinear Dynamics, Helleman, R. H. G. (ed.), New York Academy of Sciences, New York, 1980.
    • (1980) Nonlinear Dynamics
    • Ueda, Y.1
  • 78
    • 33846893200 scopus 로고    scopus 로고
    • Oscillation of a Differential Equation with Fractional Delay and Piecewise Constant Arguments
    • Wang, Y. and Yan, J., “Oscillation of a Differential Equation with Fractional Delay and Piecewise Constant Arguments,” Computers and Mathematics with Applications, Vol. 52, pp. 1099-1106, 2006.
    • (2006) Computers and Mathematics with Applications , vol.52 , pp. 1099-1106
    • Wang, Y.1    Yan, J.2
  • 81
    • 0039116174 scopus 로고
    • Oscillatory and Nonoscillatory Properties of First Order Differential Equations with Piecewise Constant Deviating Arguments
    • Zhang, B. G., and Parhi, N. “Oscillatory and Nonoscillatory Properties of First Order Differential Equations with Piecewise Constant Deviating Arguments,” Journal of Mathematical Analysis and Applications, Vol. 139, pp. 23-25, 1989.
    • (1989) Journal of Mathematical Analysis and Applications , vol.139 , pp. 23-25
    • Zhang, B.G.1    Parhi, N.2
  • 82
    • 0001224680 scopus 로고
    • Oscillatory Properties of First Order Linear Functional Differential Equations
    • Aftabizadeh, A. R., Wiener, J., “Oscillatory Properties of First Order Linear Functional Differential Equations,” Applied Analysis, Vol. 20, pp. 165-187, 1985.
    • (1985) Applied Analysis , vol.20 , pp. 165-187
    • Aftabizadeh, A.R.1    Wiener, J.2
  • 83
    • 0000327582 scopus 로고
    • Oscillatory and Periodic Solutions for Systems of Two First Order Linear Differential Equations with Piecewise Constant Argument
    • Aftabizadeh, A. R. and Wiener, J., “Oscillatory and Periodic Solutions for Systems of Two First Order Linear Differential Equations with Piecewise Constant Argument,” Applicable Analysis, Vol. 26, pp. 327-338, 1988.
    • (1988) Applicable Analysis , vol.26 , pp. 327-338
    • Aftabizadeh, A.R.1    Wiener, J.2
  • 84
    • 85126405797 scopus 로고
    • Addison-Wesley Publishing Company, Inc., Reading, Massachusetts
    • Bear, H. S., Differential Equations, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1962.
    • (1962) Differential Equations
    • Bear, H.S.1
  • 88
    • 85126406702 scopus 로고
    • On Oscillatory Motion of a Spring-Mass System Subjected to Piecewise Constant Forces
    • Dai, L. and Singh, M. C., “On Oscillatory Motion of a Spring-Mass System Subjected to Piecewise Constant Forces,” Proceedings of Thirteenth Canadian Congress of Applied Mechanics, Vol. 1, pp. 288-289, 1991.
    • (1991) Proceedings of Thirteenth Canadian Congress of Applied Mechanics , vol.1 , pp. 288-289
    • Dai, L.1    Singh, M.C.2
  • 90
    • 0028761203 scopus 로고
    • On Oscillatory Motion of Spring-Mass Systems Subjected to Piecewise Constant Forces
    • Dai, L., Singh, M. C., “On Oscillatory Motion of Spring-Mass Systems Subjected to Piecewise Constant Forces,” Journal of Sound and Vibration Vol. 173, pp. 217-232, 1994.
    • (1994) Journal of Sound and Vibration , vol.173 , pp. 217-232
    • Dai, L.1    Singh, M.C.2
  • 91
    • 0037809833 scopus 로고    scopus 로고
    • A New Approach with Piecewise-Constant Arguments to Approximate and Numerical Solutions of Oscillatory Problems
    • Dai, L. and Singh, M. C., “A New Approach with Piecewise-Constant Arguments to Approximate and Numerical Solutions of Oscillatory Problems,” Journal of Sound and Vibration, Vol. 263, No. 3, pp. 535-548, 2003.
    • (2003) Journal of Sound and Vibration , vol.263 , Issue.3 , pp. 535-548
    • Dai, L.1    Singh, M.C.2
  • 92
    • 0022676712 scopus 로고
    • On the Understanding of Chaos in Duffings Equation Including a Comparison with Experiment,”
    • Dowell, E. H., Pezeshki, C., “On the Understanding of Chaos in Duffing’s Equation Including a Comparison with Experiment,” ASME Journal of Applied Mechanics, Vol. 53, pp. 5-9, 1986.
    • (1986) ASME Journal of Applied Mechanics , vol.53 , pp. 5-9
    • Dowell, E.H.1    Pezeshki, C.2
  • 93
    • 0000507209 scopus 로고
    • De Integratione Aequationum Differentialium Altiorum Graduum
    • Euler, L., “De Integratione Aequationum Differentialium Altiorum Graduum,” Miscellanea Berdinensia, Vol. 7, pp. 193-242, 1743.
    • (1743) Miscellanea Berdinensia , vol.7 , pp. 193-242
    • Euler, L.1
  • 94
    • 84968519032 scopus 로고
    • Variation of Parameters Formula for the Equation of Cooke and Wiener
    • Jayasree, K. N. and Deo, S. G., “Variation of Parameters Formula for the Equation of Cooke and Wiener,” Proceedings of the American Mathematical Society, Vol. 112, No. 1. pp. 75-80, 1991.
    • (1991) Proceedings of the American Mathematical Society , vol.112 , Issue.1 , pp. 75-80
    • Jayasree, K.N.1    Deo, S.G.2
  • 95
    • 0004045886 scopus 로고
    • Addison-Wesley Publishing Company, Inc., Reading, Massachusetts
    • Johnson, L. W. and Riess, R. D., Numerical Analysis, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1982.
    • (1982) Numerical Analysis
    • Johnson, L.W.1    Riess, R.D.2
  • 97
    • 0024281664 scopus 로고
    • Direct Method for the Steady State Response of Structures
    • Leung, A. Y. T., “Direct Method for the Steady State Response of Structures,” Journal of Sound and Vibration, Vol. 124, No. 1, pp. 135-139, 1988.
    • (1988) Journal of Sound and Vibration , vol.124 , Issue.1 , pp. 135-139
    • Leung, A.Y.T.1
  • 106
    • 38249022581 scopus 로고
    • Oscillations in Systems of Differential Equations with Piecewise Constant Argument
    • Wiener, J. and Cooke, K. L., “Oscillations in Systems of Differential Equations with Piecewise Constant Argument,” Journal of Mathematical Analysis and Applications, Vol. 137, pp. 221-239, 1989.
    • (1989) Journal of Mathematical Analysis and Applications , vol.137 , pp. 221-239
    • Wiener, J.1    Cooke, K.L.2
  • 107
    • 0039116174 scopus 로고
    • Oscillatory and Nonoscillatory Properties of First Order Differential Equations with Piecewise Constant Deviating Arguments
    • Zhang, B. G., and Parhi, N. “Oscillatory and Nonoscillatory Properties of First Order Differential Equations with Piecewise Constant Deviating Arguments,” Journal of Mathematical Analysis and Applications, Vol. 139, pp. 23-25, 1989.
    • (1989) Journal of Mathematical Analysis and Applications , vol.139 , pp. 23-25
    • Zhang, B.G.1    Parhi, N.2
  • 108
    • 0032353463 scopus 로고    scopus 로고
    • A Class of Second-Order Runge-Kutta Methods for Numerical Solution of Stochastic Differential Equations
    • Abukhaled, M. I. and Allen, E. J., “A Class of Second-Order Runge-Kutta Methods for Numerical Solution of Stochastic Differential Equations,” Stochastic Analysis and Applications, Vol. 16, pp. 977-992, 1998.
    • (1998) Stochastic Analysis and Applications , vol.16 , pp. 977-992
    • Abukhaled, M.I.1    Allen, E.J.2
  • 109
    • 0041486883 scopus 로고
    • On the Weakly Damped Harmonic Oscillator
    • Baum, H. R., “On the Weakly Damped Harmonic Oscillator,” Quarterly of Applied Mathematics, Vol. 30, pp. 573-576, 1972.
    • (1972) Quarterly of Applied Mathematics , vol.30 , pp. 573-576
    • Baum, H.R.1
  • 112
    • 0028761203 scopus 로고
    • On Oscillatory Motion of Spring-Mass Systems Subjected to Piecewise Constant Forces
    • Dai, L. and Singh, M. C., “On Oscillatory Motion of Spring-Mass Systems Subjected to Piecewise Constant Forces,” Journal of Sound and Vibration, Vol. 173, pp. 217-233, 1994.
    • (1994) Journal of Sound and Vibration , vol.173 , pp. 217-233
    • Dai, L.1    Singh, M.C.2
  • 113
    • 0031185446 scopus 로고    scopus 로고
    • An Analytical and Numerical Method for Solving Linear and Nonlinear Vibration Problems
    • Dai, L. and Singh, M. C., “An Analytical and Numerical Method for Solving Linear and Nonlinear Vibration Problems,” International Journal of Solids and Structures, Vol. 34, pp. 2709-2731, 1997.
    • (1997) International Journal of Solids and Structures , vol.34 , pp. 2709-2731
    • Dai, L.1    Singh, M.C.2
  • 114
    • 0001391381 scopus 로고    scopus 로고
    • Periodic, Quasiperiodic and Chaotic Behavior of a Driven Froude Pendulum
    • Dai, L. and Singh, M. C., “Periodic, Quasiperiodic and Chaotic Behavior of a Driven Froude Pendulum,” International Journal of Nonlinear Mechanics, Vol. 33, pp. 947-965, 1998.
    • (1998) International Journal of Nonlinear Mechanics , vol.33 , pp. 947-965
    • Dai, L.1    Singh, M.C.2
  • 116
    • 0022676712 scopus 로고
    • On the Understanding of Chaos in Duffings Equation Including a Comparison with Experiment,”
    • Dowell, E. H. and Pezeshki, C., “On the Understanding of Chaos in Duffing’s Equation Including a Comparison with Experiment,” ASME Journal of Applied Mechanics, Vol. 53, pp. 5-9, 1986.
    • (1986) ASME Journal of Applied Mechanics , vol.53 , pp. 5-9
    • Dowell, E.H.1    Pezeshki, C.2
  • 118
    • 0001230012 scopus 로고
    • Intermittent Chaos and Low-Frequency Noise in the Driven Damped Pendulum
    • Gwinn, E. G. and Westervelt, R. M., “Intermittent Chaos and Low-Frequency Noise in the Driven Damped Pendulum,” Physical Review, Letters, Vol. 55, No. 15, pp. 1613-1616, 1985.
    • (1985) Physical Review, Letters , vol.55 , Issue.15 , pp. 1613-1616
    • Gwinn, E.G.1    Westervelt, R.M.2
  • 120
    • 84913798212 scopus 로고
    • Steady State Vibrations in Systems having Arbitrary Restoring and Damping Forces
    • Polytechnic Institute of Brooklyn
    • Klotter, K., “Steady State Vibrations in Systems having Arbitrary Restoring and Damping Forces,” in Symposium on Nonlinear Circuit Analysis, Polytechnic Institute of Brooklyn, pp. 234-257, 1953.
    • (1953) Symposium on Nonlinear Circuit Analysis , pp. 234-257
    • Klotter, K.1
  • 121
    • 0006451452 scopus 로고
    • Beitrag zur näherungsweisen Integration totaler Differentialgleichungen
    • Kutta, W., “Beitrag zur näherungsweisen Integration totaler Differentialgleichungen,” Zeitschrift fur Mathematik und Physik, Vol. 46, pp. 435-453, 1901.
    • (1901) Zeitschrift Fur Mathematik Und Physik , vol.46 , pp. 435-453
    • Kutta, W.1
  • 122
    • 85003340059 scopus 로고
    • Optimal Predictor-Corrector Method for Systems of Second-order Differential Equations
    • Morino, L., Leech, J. W. and Witmer, E. A., “Optimal Predictor-Corrector Method for Systems of Second-order Differential Equations,” AIAA Journal, Vol. 12, No. 10, pp. 1343-1347, 1974.
    • (1974) AIAA Journal , vol.12 , Issue.10 , pp. 1343-1347
    • Morino, L.1    Leech, J.W.2    Witmer, E.A.3
  • 129
    • 0012650693 scopus 로고
    • Ueber die numerische Auflösung totaler Differential gleichungen
    • Runge, C., “Ueber die numerische Auflösung totaler Differential gleichungen,” Mathematische Annalen, Vol. 46, pp. 167-178, 1895.
    • (1895) Mathematische Annalen , vol.46 , pp. 167-178
    • Runge, C.1
  • 131
    • 0001804640 scopus 로고
    • Steady Motions Exhibited by Duffings Equation: A Picture Book of Regular and Chaotic Motions,”
    • Philadelphia: SIAM
    • Ueda, Y., “Steady Motions Exhibited by Duffing’s Equation: A Picture Book of Regular and Chaotic Motions,” in New Approaches to Nonlinear Problems in Dynamics, (editor P.J. Holmes), Philadelphia: SIAM, pp. 311-322, 1980.
    • (1980) New Approaches to Nonlinear Problems in Dynamics, (Editor P.J. Holmes) , pp. 311-322
    • Ueda, Y.1
  • 133
    • 0033207809 scopus 로고    scopus 로고
    • Runge-Kutta Methods for Linear Ordinary Differential Equations
    • Zingg, D. W. and Chisholm, T. T., “Runge-Kutta Methods for Linear Ordinary Differential Equations,” Applied Numerical Mathematics, Vol. 31, pp. 227-238, 1999.
    • (1999) Applied Numerical Mathematics , vol.31 , pp. 227-238
    • Zingg, D.W.1    Chisholm, T.T.2
  • 134
    • 0022522584 scopus 로고
    • Internal Resonance Effects-Simulation versus Analytical Methods Results
    • Bajkowski, J. and Szemplinska-Stupnicka, W., “Internal Resonance Effects-Simulation versus Analytical Methods Results,” Journal of Sound and Vibration, Vol. 104, pp. 259-275, 1986.
    • (1986) Journal of Sound and Vibration , vol.104 , pp. 259-275
    • Bajkowski, J.1    Szemplinska-Stupnicka, W.2
  • 135
    • 0001315863 scopus 로고
    • Application of the Incremental Harmonic Balance Method to Cubic Non-Linearity Systems
    • Cheung, Y. K., Chen, S. H. and Lau, S. L., “Application of the Incremental Harmonic Balance Method to Cubic Non-Linearity Systems,” Journal of Sound and Vibration, Vol. 140, No. 2, pp. 273-286, 1990.
    • (1990) Journal of Sound and Vibration , vol.140 , Issue.2 , pp. 273-286
    • Cheung, Y.K.1    Chen, S.H.2    Lau, S.L.3
  • 136
    • 0037809833 scopus 로고    scopus 로고
    • A New Approach with Piecewise Constant Arguments to Approximate and Numerical Solutions of Oscillatory Problems
    • Dai, L. and Singh, M. C., “A New Approach with Piecewise Constant Arguments to Approximate and Numerical Solutions of Oscillatory Problems,” Journal of Sound and Vibration, Vol. 263, No. 3, pp. 535-548, 2003.
    • (2003) Journal of Sound and Vibration , vol.263 , Issue.3 , pp. 535-548
    • Dai, L.1    Singh, M.C.2
  • 137
    • 33645952390 scopus 로고    scopus 로고
    • Semi-Analytical and Numerical Solutions of Multi-Degree-of-Freedom Nonlinear Oscillation Systems with Linear Coupling
    • Dai, L, Xu, L and Han, Q, “Semi-Analytical and Numerical Solutions of Multi-Degree-of-Freedom Nonlinear Oscillation Systems with Linear Coupling,” Communications in Nonlinear Science and Numerical Simulations, Vol. 11, pp. 831-844, 2006.
    • (2006) Communications in Nonlinear Science and Numerical Simulations , vol.11 , pp. 831-844
    • Dai, L.1    Xu, L.2    Han, Q.3
  • 139
    • 0038400822 scopus 로고    scopus 로고
    • Runge-Kutta Methods for Quadratic Ordinary Differential Equations
    • Iserles, A., Ramaswami, G. and Sofroniou M., “Runge-Kutta Methods for Quadratic Ordinary Differential Equations,” BIT—Numerical Mathematics, Vol. 38, pp. 315-336, 1998.
    • (1998) BIT—Numerical Mathematics , vol.38 , pp. 315-336
    • Iserles, A.1    Ramaswami, G.2    Sofroniou, M.3
  • 143
    • 0031142354 scopus 로고    scopus 로고
    • A Quantitative Stability and Bifurcation Analyses of a Generalized Duffing Oscillator with Strong Nonlinearity
    • Luo, A. C. J. and Han, R. P. S., “A Quantitative Stability and Bifurcation Analyses of a Generalized Duffing Oscillator with Strong Nonlinearity,” Journal of Franklin Institute,” Vol. 334B, pp. 447-459, 1997.
    • (1997) Journal of Franklin Institute,” , vol.334B , pp. 447-459
    • Luo, A.C.J.1    Han, R.P.S.2
  • 144
    • 0028392575 scopus 로고
    • A Global Analysis of an Harmonically Excited Spring-Pendulum System with Internal Resonance
    • Lee, W. K. and Hsu, C. S., “A Global Analysis of an Harmonically Excited Spring-Pendulum System with Internal Resonance,” Journal of Sound and Vibration, Vol. 171, No. 3, pp. 335-359, 1994.
    • (1994) Journal of Sound and Vibration , vol.171 , Issue.3 , pp. 335-359
    • Lee, W.K.1    Hsu, C.S.2
  • 145
    • 0015672134 scopus 로고
    • Nonlinear Coupling of Pitch and Roll Modes in Ship Motions
    • Nayfeh, A. H., Mook, D. T. and Marshall, L. R., “Nonlinear Coupling of Pitch and Roll Modes in Ship Motions,” Journal of Hydronautics, Vol. 7, No. 4, pp. 145-152, 1973.
    • (1973) Journal of Hydronautics , vol.7 , Issue.4 , pp. 145-152
    • Nayfeh, A.H.1    Mook, D.T.2    Marshall, L.R.3
  • 150
    • 0033207809 scopus 로고    scopus 로고
    • Runge-Kutta Methods for Linear Ordinary Differential Equations
    • Zingg, D. W. and Chisholm, T. T., “Runge-Kutta Methods for Linear Ordinary Differential Equations,” Applied Numerical Mathematics, Vol. 31, pp. 227-238, 1999.
    • (1999) Applied Numerical Mathematics , vol.31 , pp. 227-238
    • Zingg, D.W.1    Chisholm, T.T.2
  • 154
    • 0022128940 scopus 로고
    • Chaotic Mode Competition in Parametrically Forced Surface Waves
    • Ciliberto, S. and Gollub, J. P., “Chaotic Mode Competition in Parametrically Forced Surface Waves,” Journal of Fluid Mechanics, Vol. 158, pp. 381-398, 1985.
    • (1985) Journal of Fluid Mechanics , vol.158 , pp. 381-398
    • Ciliberto, S.1    Gollub, J.P.2
  • 156
    • 0031455025 scopus 로고    scopus 로고
    • Diagnosis of Periodic and Chaotic Responses in Vibratory Systems
    • Dai, L. and Singh, M. C., “Diagnosis of Periodic and Chaotic Responses in Vibratory Systems,” Journal of Acoustic Society of America, Vol. 102, No. 6, pp. 3361-3371, 1997.
    • (1997) Journal of Acoustic Society of America , vol.102 , Issue.6 , pp. 3361-3371
    • Dai, L.1    Singh, M.C.2
  • 157
    • 0037809833 scopus 로고    scopus 로고
    • A New Approach with Piecewise-Constant Arguments to Approximate and Numerical Solutions of Oscillatory Problems
    • Dai, L. and Singh, M. C., “A New Approach with Piecewise-Constant Arguments to Approximate and Numerical Solutions of Oscillatory Problems,” Journal of Sound and Vibration, Vol. 263, No. 3, pp. 535-548, 2003.
    • (2003) Journal of Sound and Vibration , vol.263 , Issue.3 , pp. 535-548
    • Dai, L.1    Singh, M.C.2
  • 159
    • 48749145669 scopus 로고
    • The Dimension of Chaotic Attractors
    • Farmer, J. D., Ott, E. and Yorke, J. A., “The Dimension of Chaotic Attractors,” Physica, Vol. 7D, pp. 153-170, 1983.
    • (1983) Physica , vol.7D , pp. 153-170
    • Farmer, J.D.1    Ott, E.2    Yorke, J.A.3
  • 160
    • 0002099734 scopus 로고
    • General and Use of Orthogonal Polynomials for Fitting Data with a Digital Computer
    • Forsythe, G. E., “General and Use of Orthogonal Polynomials for Fitting Data with a Digital Computer,” SIAM Journal on Applied Mathematics, Vol. 5, pp. 74-88, 1957.
    • (1957) SIAM Journal on Applied Mathematics , vol.5 , pp. 74-88
    • Forsythe, G.E.1
  • 161
    • 0001230012 scopus 로고
    • Intermittent Chaos and Low-Frequency Noise in the Driven Damped Pendulum
    • Gwinn, E. G. and Westervelt, R. M., “Intermittent Chaos and Low-Frequency Noise in the Driven Damped Pendulum,” Physical Review Letters, Vol. 55, No. 15, pp. 1613-1616, 1985.
    • (1985) Physical Review Letters , vol.55 , Issue.15 , pp. 1613-1616
    • Gwinn, E.G.1    Westervelt, R.M.2
  • 163
    • 4243798800 scopus 로고
    • Fractal Basin Boundaries and Intermittency in the Driven Damped Pendulum
    • Gwinn, E. G. and Westervelt, R. M., “Fractal Basin Boundaries and Intermittency in the Driven Damped Pendulum,” Physical Review A, Vol. 33, pp. 4143-4155, 1986.
    • (1986) Physical Review A , vol.33 , pp. 4143-4155
    • Gwinn, E.G.1    Westervelt, R.M.2
  • 172
    • 9544238117 scopus 로고    scopus 로고
    • Computing Lyapunov-Exponents of Continuous Dynamical Systems: Method of Lyapunov Vectors
    • Lu, J., Yang, G., Oh, H. and Luo, A.J., “Computing Lyapunov-Exponents of Continuous Dynamical Systems: Method of Lyapunov Vectors,” Chaos, Solitons and Fractals, Vol. 23, pp. 1879-1892, 2005.
    • (2005) Chaos, Solitons and Fractals , vol.23 , pp. 1879-1892
    • Lu, J.1    Yang, G.2    Oh, H.3    Luo, A.J.4
  • 173
    • 45949127771 scopus 로고
    • Different Ways to Turbulence in Dissipative Dynamical Systems
    • Manneville, P. and Pomeau, Y., “Different Ways to Turbulence in Dissipative Dynamical Systems,” Physica, Vol. 1D, pp. 219-226, 1980.
    • (1980) Physica , vol.1D , pp. 219-226
    • Manneville, P.1    Pomeau, Y.2
  • 174
    • 0010944527 scopus 로고
    • Experimental Models for Strange Attractor Vibration in Elastic Systems
    • Holmes, P. J. (ed.)
    • Moon, F. C., “Experimental Models for Strange Attractor Vibration in Elastic Systems,” in New Approaches to Nonlinear Problems in Dynamics, Holmes, P. J. (ed.), pp. 487-495, 1980(A).
    • (1980) New Approaches to Nonlinear Problems in Dynamics , pp. 487-495
    • Moon, F.C.1
  • 175
    • 0019064545 scopus 로고
    • Experiments on Chaotic Motions of a Forced Nonlinear Oscillator: Strange Attractors
    • Moon, F. C., “Experiments on Chaotic Motions of a Forced Nonlinear Oscillator: Strange Attractors,” ASME Journal of Applied Mechanics, Vol. 47, pp. 638-644, 1980(B).
    • (1980) ASME Journal of Applied Mechanics , vol.47 , pp. 638-644
    • Moon, F.C.1
  • 176
    • 0003478955 scopus 로고
    • John Wiley & Sons, Inc., New York
    • Moon, F. C., Chaotic Vibrations, John Wiley & Sons, Inc., New York, 1987.
    • (1987) Chaotic Vibrations
    • Moon, F.C.1
  • 177
    • 84910785593 scopus 로고
    • American Society of Mechanical Engineers, New York, NY
    • Nayfeh, A.H. and Mook, D.T., Nonlinear Dynamics, American Society of Mechanical Engineers, New York, NY: 1988.
    • (1988) Nonlinear Dynamics
    • Nayfeh, A.H.1    Mook, D.T.2
  • 178
    • 12044255333 scopus 로고
    • On-Off Intermittency: A Mechanism for Bursting
    • Platt, N, Spiegel, E.A. and Tresser, C., “On-Off Intermittency: A Mechanism for Bursting,” Physical Review Letters, Vol. 70, pp. 279-282, 1993.
    • (1993) Physical Review Letters , vol.70 , pp. 279-282
    • Platt, N.1    Spiegel, E.A.2    Tresser, C.3
  • 180
    • 0036926475 scopus 로고    scopus 로고
    • Invariant Measures and Lyapunov-Exponents for Stochastic Mathieu System
    • Rong, H., Meng, G., Wang, X., Xu, W. and Fang, T., “Invariant Measures and Lyapunov-Exponents for Stochastic Mathieu System,” Nonlinear Dynamics, Vol. 30, pp. 313-321, 2002.
    • (2002) Nonlinear Dynamics , vol.30 , pp. 313-321
    • Rong, H.1    Meng, G.2    Wang, X.3    Xu, W.4    Fang, T.5
  • 183
    • 0038242502 scopus 로고    scopus 로고
    • Semi-Analytic Estimates of Lyapunov Exponents in Lower-Dimensional Systems
    • Terzic, B. and Kandrup, H.E., “Semi-Analytic Estimates of Lyapunov Exponents in Lower-Dimensional Systems,” Physics Letters, A311, 165, pp. 1-6, 2003.
    • (2003) Physics Letters , vol.A311 , Issue.165 , pp. 1-6
    • Terzic, B.1    Kandrup, H.E.2
  • 186
    • 33746672747 scopus 로고
    • Random Transitional Phenomena in the System Governed by Duffings Equation,”
    • Ueda, Y., “Random Transitional Phenomena in the System Governed by Duffing’s Equation,” Journal of Statistical Physics, Vol. 20, pp. 181-196, 1979.
    • (1979) Journal of Statistical Physics , vol.20 , pp. 181-196
    • Ueda, Y.1
  • 187
    • 0001804640 scopus 로고
    • Steady motions exhibited by Duffings equation: A picture book of regular and chaotic motions
    • Holmes, P. J. (ed.), SIAM, Philadelphia
    • Ueda, Y., “Steady motions exhibited by Duffing’s equation: A picture book of regular and chaotic motions, in New Approaches to Nonlinear Problems in Dynamics, Holmes, P. J. (ed.), SIAM, Philadelphia, pp. 311-322, 1980.
    • (1980) New Approaches to Nonlinear Problems in Dynamics , pp. 311-322
    • Ueda, Y.1
  • 189
    • 0008494528 scopus 로고
    • Determining Lyapunov Exponents from a Fine Series
    • Wolf, A., Swift, J. B., Swinney, H. L. and Vastano, J. A., “Determining Lyapunov Exponents from a Fine Series,” Physica, Vol. 16D, pp. 285-317, 1985.
    • (1985) Physica , vol.16D , pp. 285-317
    • Wolf, A.1    Swift, J.B.2    Swinney, H.L.3    Vastano, J.A.4
  • 190
    • 34249704007 scopus 로고    scopus 로고
    • Vibration Analysis and Bifurcations in the Self-Sustained Electromechanical System with Multiple Functions
    • Yamapi, R. and Aziz-Alaoui, M.A., “Vibration Analysis and Bifurcations in the Self-Sustained Electromechanical System with Multiple Functions,” Communications in Nonlinear Science and Numerical Simulation, Vol. 12, No. 8, pp. 1534-1549, 2007.
    • (2007) Communications in Nonlinear Science and Numerical Simulation , vol.12 , Issue.8 , pp. 1534-1549
    • Yamapi, R.1    Aziz-Alaoui, M.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.