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Volumn 45, Issue 6, 2012, Pages 737-752

Synchronization of fractional order chaotic systems using active control method

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; SYNCHRONIZATION;

EID: 84860168517     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2012.02.004     Document Type: Article
Times cited : (167)

References (61)
  • 4
    • 0004269732 scopus 로고
    • Reprinted from 1798 edition Johnson London, as Malthus population: the first essay. Ann Arbor Paper-backs. Ann Arbor Michigan, USA: University of Michigan
    • Malthus TR. An essay on the principle of population. Reprinted from 1798 edition Johnson London, as Malthus population: the first essay. Ann Arbor Paper-backs. Ann Arbor Michigan, USA: University of Michigan; 1959.
    • (1959) An Essay on the Principle of Population
    • Malthus, T.R.1
  • 5
    • 0001119103 scopus 로고
    • Notice sur la loi que la population suit dans son accroissement
    • P.F. Verhulst Notice sur la loi que la population suit dans son accroissement Corr Math Phys 10 1838 113 121
    • (1838) Corr Math Phys , vol.10 , pp. 113-121
    • Verhulst, P.F.1
  • 7
    • 0002604954 scopus 로고
    • Variazioni e fluttuazioni del numero di individui in specie
    • V. Volterra Variazioni e fluttuazioni del numero di individui in specie Mem Accd Linc 2 1926 31 113
    • (1926) Mem Accd Linc , vol.2 , pp. 31-113
    • Volterra, V.1
  • 8
    • 0345748121 scopus 로고
    • Explosive route to chaos through a fractal torus in a generalized Lotka-Volterra model
    • N. Samardzija, and L.D. Greller Explosive route to chaos through a fractal torus in a generalized Lotka-Volterra model Bull Math Bio 50 1988 465 491
    • (1988) Bull Math Bio , vol.50 , pp. 465-491
    • Samardzija, N.1    Greller, L.D.2
  • 9
    • 0002963435 scopus 로고
    • Double strange attractors in rigid body motion
    • R.B. Leipnik, and T.A. Newton Double strange attractors in rigid body motion Phys Lett A 86 1981 63 67
    • (1981) Phys Lett A , vol.86 , pp. 63-67
    • Leipnik, R.B.1    Newton, T.A.2
  • 10
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • E.N. Lorenz Deterministic nonperiodic flow J Atmos Sci 20 1963 130 141
    • (1963) J Atmos Sci , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 11
    • 0000432310 scopus 로고
    • Chaos in the segmented disc dynamo
    • E. Knobloch Chaos in the segmented disc dynamo Phys Lett A 82 1981 439 440
    • (1981) Phys Lett A , vol.82 , pp. 439-440
    • Knobloch, E.1
  • 13
    • 72749114026 scopus 로고    scopus 로고
    • Peristaltic flow of viscoelastic fluid with fractional maxwell model through a channel
    • S. Das, D. Tripathi, and S.K. Pandey Peristaltic flow of viscoelastic fluid with fractional maxwell model through a channel Appl Math Comput 215 2010 3645 3654
    • (2010) Appl Math Comput , vol.215 , pp. 3645-3654
    • Das, S.1    Tripathi, D.2    Pandey, S.K.3
  • 14
    • 77953342903 scopus 로고    scopus 로고
    • Application of fractional calculus in the theory of viscoelasticity
    • E. Soczkiewicz Application of fractional calculus in the theory of viscoelasticity Mol Quant Acoust 23 2002 397 404
    • (2002) Mol Quant Acoust , vol.23 , pp. 397-404
    • Soczkiewicz, E.1
  • 15
    • 1342264358 scopus 로고    scopus 로고
    • Calculation of the tensile and flexural strength of disordered materials using fractional calculus
    • A. Carpinteri, P. Cornetti, and K.M. Kolwankar Calculation of the tensile and flexural strength of disordered materials using fractional calculus Chaos Soliton Fract 21 2004 623 632
    • (2004) Chaos Soliton Fract , vol.21 , pp. 623-632
    • Carpinteri, A.1    Cornetti, P.2    Kolwankar, K.M.3
  • 16
    • 4444254886 scopus 로고    scopus 로고
    • Fractional calculus in bioengineering. Part 3
    • R.L. Magin Fractional calculus in bioengineering. Part 3 Crit Rev Biomed Eng 32 2004 195 377
    • (2004) Crit Rev Biomed Eng , vol.32 , pp. 195-377
    • Magin, R.L.1
  • 18
    • 76449091415 scopus 로고    scopus 로고
    • Fractional calculus models of complex dynamics in biological tissues
    • R.L. Magin Fractional calculus models of complex dynamics in biological tissues Comput Math Appl 59 2010 1585 1593
    • (2010) Comput Math Appl , vol.59 , pp. 1585-1593
    • Magin, R.L.1
  • 19
    • 52349105913 scopus 로고    scopus 로고
    • Modeling the cardiac tissue electrode interface using fractional calculus
    • R.L. Magin Modeling the cardiac tissue electrode interface using fractional calculus J Vib Cont 14 2008 1431 1442
    • (2008) J Vib Cont , vol.14 , pp. 1431-1442
    • Magin, R.L.1
  • 20
    • 0141974618 scopus 로고    scopus 로고
    • Fractional diffusion processes: Probability distributions and continuous time random walk
    • G. Rangarajan, M. Ding, Springer-verlag Berlin [Lecture Notes in Physics, No. 621]
    • R. Gorenflo, and F. Mainardi Fractional diffusion processes: probability distributions and continuous time random walk G. Rangarajan, M. Ding, Processes with long range correlations 2003 Springer-verlag Berlin 148 166 [Lecture Notes in Physics, No. 621]
    • (2003) Processes with Long Range Correlations , pp. 148-166
    • Gorenflo, R.1    Mainardi, F.2
  • 21
    • 34047155650 scopus 로고    scopus 로고
    • Continuous-time random walk and parametric subordination in fractional diffusion
    • DOI 10.1016/j.chaos.2007.01.052, PII S0960077907000926
    • R. Gorenflo, F. Mainardi, and A. Vivoli Continuous-time random walk and parametric subordination in fractional diffusion Chaos Soliton Fract 34 1 2007 87 103 (Pubitemid 46529249)
    • (2007) Chaos, Solitons and Fractals , vol.34 , Issue.1 , pp. 87-103
    • Gorenflo, R.1    Mainardi, F.2    Vivoli, A.3
  • 24
    • 14844323003 scopus 로고    scopus 로고
    • A falling body problem through the air in view of the fractional derivative approach
    • DOI 10.1016/j.physa.2004.11.041, PII S0378437104014864
    • K.S. Fa A falling body problem through the air in view of the fractional derivative approach Physica A 350 2005 199 206 (Pubitemid 40338088)
    • (2005) Physica A: Statistical Mechanics and its Applications , vol.350 , Issue.2-4 , pp. 199-206
    • Fa, K.S.1
  • 25
    • 79953170542 scopus 로고    scopus 로고
    • Front dynamical in fractional-order epidemic models
    • E. Hanert, E. Schumacher, and E. Deleersnijder Front dynamical in fractional-order epidemic models J Theor Biol 279 2011 9 16
    • (2011) J Theor Biol , vol.279 , pp. 9-16
    • Hanert, E.1    Schumacher, E.2    Deleersnijder, E.3
  • 26
    • 67549148317 scopus 로고    scopus 로고
    • A fractional order differential equation model of HIV infection of CD4+ T cell
    • Y. Ding, and H. Ye A fractional order differential equation model of HIV infection of CD4+ T cell Math Comput Model 50 2009 386 392
    • (2009) Math Comput Model , vol.50 , pp. 386-392
    • Ding, Y.1    Ye, H.2
  • 27
    • 33750295344 scopus 로고    scopus 로고
    • Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models
    • DOI 10.1016/j.jmaa.2006.01.087, PII S0022247X06000801
    • E. Ahmed, A.M.A. EL-Sayed, and H.A.A. EL-Saka Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models J Math Anal Appl 325 2007 542 553 (Pubitemid 44615337)
    • (2007) Journal of Mathematical Analysis and Applications , vol.325 , Issue.1 , pp. 542-553
    • Ahmed, E.1    El-Sayed, A.M.A.2    El-Saka, H.A.A.3
  • 28
    • 70349602750 scopus 로고    scopus 로고
    • A fractional predator-prey model and its solution
    • S. Das, P.K. Gupta, and Rajeev A fractional predator-prey model and its solution Int J Nonlin Sci Numer Simul 10 2009 873 876
    • (2009) Int J Nonlin Sci Numer Simul , vol.10 , pp. 873-876
    • Das, S.1    Gupta, P.K.2    Rajeev3
  • 29
    • 79952197225 scopus 로고    scopus 로고
    • A mathematical model on fractional Lotka-Volterra equations
    • S. Das, and P.K. Gupta A mathematical model on fractional Lotka-Volterra equations J Theor Biol 277 2011 1 6
    • (2011) J Theor Biol , vol.277 , pp. 1-6
    • Das, S.1    Gupta, P.K.2
  • 31
    • 0041384356 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional order Lorenz system
    • I. Grigorenko, and E. Grigorenko Chaotic dynamics of the fractional order Lorenz system Phys Rev Lett 91 2003 034101 034104
    • (2003) Phys Rev Lett , vol.91 , pp. 034101-034104
    • Grigorenko, I.1    Grigorenko, E.2
  • 32
    • 67649861441 scopus 로고    scopus 로고
    • Dynamical analysis of a fractional order Lorenz chaotic system
    • Y. Yu, X.L. Li, S. Wang, and J. Yu Dynamical analysis of a fractional order Lorenz chaotic system Chaos Soliton Fract 42 2009 1181 1189
    • (2009) Chaos Soliton Fract , vol.42 , pp. 1181-1189
    • Yu, Y.1    Li, X.L.2    Wang, S.3    Yu, J.4
  • 33
    • 77955018368 scopus 로고    scopus 로고
    • Bifurcations of fractional-order diffusionless Lorenz system
    • K. Sun, and J.C. Sprott Bifurcations of fractional-order diffusionless Lorenz system Electron J Theor Phys 6 2009 123 134
    • (2009) Electron J Theor Phys , vol.6 , pp. 123-134
    • Sun, K.1    Sprott, J.C.2
  • 34
    • 40549104097 scopus 로고    scopus 로고
    • Parametric analysis & a fractional order Newton-Leipnik system
    • Y. Kang, K.T. Lin, J.H. Chen, L.J. Sheu, and H.K. Chen Parametric analysis & a fractional order Newton-Leipnik system J Phys Conf Ser 96 2008 012140
    • (2008) J Phys Conf ser , vol.96 , pp. 012140
    • Kang, Y.1    Lin, K.T.2    Chen, J.H.3    Sheu, L.J.4    Chen, H.K.5
  • 35
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • DOI 10.1023/A:1016592219341, Fractional Order Calculus and Its Applications
    • K. Diethelm, N.J. Ford, and A.B. Freed A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dyn 29 2002 3 22 (Pubitemid 34945390)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 36
    • 79961046349 scopus 로고    scopus 로고
    • Feed back control and hybrid Projective synchronization of a fractional order Newton-Leipnik system
    • K. Zhang, H. Wang, and H. Fang Feed back control and hybrid Projective synchronization of a fractional order Newton-Leipnik system Commun Nonlin Sci Numer Simul 17 2012 317 328
    • (2012) Commun Nonlin Sci Numer Simul , vol.17 , pp. 317-328
    • Zhang, K.1    Wang, H.2    Fang, H.3
  • 37
    • 0343689904 scopus 로고
    • Synchronization in chaotic systems
    • L.M. Pecora, and T.L. Carroll Synchronization in chaotic systems Phys Rev Lett 64 1990 821 824
    • (1990) Phys Rev Lett , vol.64 , pp. 821-824
    • Pecora, L.M.1    Carroll, T.L.2
  • 38
    • 0033609387 scopus 로고    scopus 로고
    • Complex dynamics and phase synchronization in spatially extended ecological systems
    • DOI 10.1038/20676
    • B. Blasius, A. Huppert, and L. Stone Complex dynamics and phase synchronization in spatially extended ecological system Nature 399 1999 354 359 (Pubitemid 29318132)
    • (1999) Nature , vol.399 , Issue.6734 , pp. 354-359
    • Blasius, B.1    Huppert, A.2    Stone, L.3
  • 40
    • 4244104642 scopus 로고
    • D-phasing and bursting in coupled neural oscillators
    • S.K. Han, C. Kerrer, and Y. Kuramoto D-phasing and bursting in coupled neural oscillators Phys Rev Lett 75 1995 3190 3193
    • (1995) Phys Rev Lett , vol.75 , pp. 3190-3193
    • Han, S.K.1    Kerrer, C.2    Kuramoto, Y.3
  • 41
    • 12044251580 scopus 로고
    • Circuit implementation of synchronized chaos with application to communication
    • K.M. Cuomo, and A.V. Oppenheim Circuit implementation of synchronized chaos with application to communication Phys Rev Lett 71 1993 65 68
    • (1993) Phys Rev Lett , vol.71 , pp. 65-68
    • Cuomo, K.M.1    Oppenheim, A.V.2
  • 42
    • 79960334316 scopus 로고    scopus 로고
    • Secure communication using a compound signal using sampled-data feedback
    • K. Murali, and M. Lakshmanan Secure communication using a compound signal using sampled-data feedback Appl Math Mech 11 2003 1309 1315
    • (2003) Appl Math Mech , vol.11 , pp. 1309-1315
    • Murali, K.1    Lakshmanan, M.2
  • 43
    • 0037043301 scopus 로고    scopus 로고
    • Parameters identification and synchronization of chaotic systems based upon adaptive control
    • S.H. Chen, and J. Lu Parameters identification and synchronization of chaotic systems based upon adaptive control Phys Lett A 299 2002 353 358
    • (2002) Phys Lett A , vol.299 , pp. 353-358
    • Chen, S.H.1    Lu, J.2
  • 44
    • 0347989162 scopus 로고    scopus 로고
    • Synchronization of chaotic systems via nonlinear control
    • L. Huang, R. Feng, and M. Wang Synchronization of chaotic systems via nonlinear control Phys Lett A 320 2004 271 275
    • (2004) Phys Lett A , vol.320 , pp. 271-275
    • Huang, L.1    Feng, R.2    Wang, M.3
  • 45
    • 4243135936 scopus 로고    scopus 로고
    • A novel criterion for delayed feedback control of time-delay chaotic systems
    • 495-01
    • J.H. Park, and O.M. Kwon A novel criterion for delayed feedback control of time-delay chaotic systems Chaos Soliton Fract 23 2005 495-01
    • (2005) Chaos Soliton Fract , vol.23
    • Park, J.H.1    Kwon, O.M.2
  • 46
    • 0036722179 scopus 로고    scopus 로고
    • Synchronization of an uncertain unified chaotic system via adaptive control
    • PII S0960077902000061
    • S.H. Chen, and J. Lu Synchronization of an uncertain unified chaotic system via adaptive control Chaos Soliton Fract 14 2002 643 647 (Pubitemid 34222496)
    • (2002) Chaos, Solitons and Fractals , vol.14 , Issue.4 , pp. 643-647
    • Chen, S.1    Lu, J.2
  • 47
    • 0037009799 scopus 로고    scopus 로고
    • Synchronization of two different systems by using generalized active control
    • M.C. Ho, and Y.C. Hung Synchronization of two different systems by using generalized active control Phys Lett A 301 2002 424 429
    • (2002) Phys Lett A , vol.301 , pp. 424-429
    • Ho, M.C.1    Hung, Y.C.2
  • 48
    • 3142716961 scopus 로고    scopus 로고
    • Chaos synchronization between two different chaotic systems using active control
    • M.T. Yassen Chaos synchronization between two different chaotic systems using active control Chaos Soliton Fract 23 2005 131 140
    • (2005) Chaos Soliton Fract , vol.23 , pp. 131-140
    • Yassen, M.T.1
  • 49
    • 22844452048 scopus 로고    scopus 로고
    • Chaos synchronization between two different chaotic dynamical systems
    • DOI 10.1016/j.chaos.2005.03.049, PII S0960077905003553
    • J.H. Park Chaos synchronization between two different chaotic dynamical systems Chaos Soliton Fract 27 2006 549 554 (Pubitemid 41037139)
    • (2006) Chaos, Solitons and Fractals , vol.27 , Issue.2 , pp. 549-554
    • Park, J.H.1
  • 50
    • 33749563875 scopus 로고    scopus 로고
    • On chaos synchronization of fractional differential equations
    • J.P. Yan, and C.P. Li On chaos synchronization of fractional differential equations Chaos Soliton Fract 32 2007 725 735
    • (2007) Chaos Soliton Fract , vol.32 , pp. 725-735
    • Yan, J.P.1    Li, C.P.2
  • 51
    • 69949102663 scopus 로고    scopus 로고
    • Chaos synchronization using active control and backstepping control: A comparative analysis
    • U.E. Vincent Chaos synchronization using active control and backstepping control: a comparative analysis Nonlin Anal Model Control 13 2008 253 261
    • (2008) Nonlin Anal Model Control , vol.13 , pp. 253-261
    • Vincent, U.E.1
  • 53
    • 18844427587 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional Lü system
    • W.H. Deng, and C.P. Li Chaos synchronization of the fractional Lü system Physica A 353 2005 61 72
    • (2005) Physica A , vol.353 , pp. 61-72
    • Deng, W.H.1    Li, C.P.2
  • 54
    • 33749553588 scopus 로고    scopus 로고
    • The synchronization of three fractional differential systems
    • C.P. Li, and J.P. Yan The synchronization of three fractional differential systems Chaos Soliton Fract 32 2007 751 757
    • (2007) Chaos Soliton Fract , vol.32 , pp. 751-757
    • Li, C.P.1    Yan, J.P.2
  • 55
    • 85126458421 scopus 로고    scopus 로고
    • Chaos in fractional-order Genesio-Tesi system and its synchronization
    • 10.1016/j.cnsns. 2011.05.03
    • M.R. Faieghi, and H. Delavari Chaos in fractional-order Genesio-Tesi system and its synchronization Commun Nonlinear Sci Numer Simul 2011 10.1016/j.cnsns. 2011.05.03
    • (2011) Commun Nonlinear Sci Numer Simul
    • Faieghi, M.R.1    Delavari, H.2
  • 56
    • 84860176654 scopus 로고    scopus 로고
    • Anti-synchronization of Li and Lu Chaotic system by active control nonlinear control
    • V. Sundarapandian Anti-synchronization of Li and Lu Chaotic system by active control nonlinear control Int J Math Sci Appl. 2011 1
    • (2011) Int J Math Sci Appl. , pp. 1
    • Sundarapandian, V.1
  • 58
    • 70449574688 scopus 로고    scopus 로고
    • Chaos in the fractional-order Lorenz system
    • X.J. Wu, and S.L. Shen Chaos in the fractional-order Lorenz system Int J Comput Math 86 2009 1274 1282
    • (2009) Int J Comput Math , vol.86 , pp. 1274-1282
    • Wu, X.J.1    Shen, S.L.2
  • 59
    • 3042709180 scopus 로고    scopus 로고
    • Multi-order fractional differential equations and their numerical solution
    • K. Diethelm, and J. Ford Multi-order fractional differential equations and their numerical solution Appl Math Comput 154 2004 621 640
    • (2004) Appl Math Comput , vol.154 , pp. 621-640
    • Diethelm, K.1    Ford, J.2


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