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Volumn , Issue , 2002, Pages 1-344

Discrete dynamical systems and difference equations with mathematica

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EID: 85057470026     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book
Times cited : (207)

References (195)
  • 1
    • 85084168098 scopus 로고
    • Difference Equations and Inequalities
    • Marcel Dekker Inc., New York
    • R. Agarwal, Difference Equations and Inequalities. Theory, Methods and Applications, Marcel Dekker Inc., New York, 1992.
    • (1992) Theory, Methods and Applications
    • Agarwal, R.1
  • 2
    • 0033229539 scopus 로고    scopus 로고
    • On the analysis of stability, bifurcation, chaos and chaos control of Kopel map
    • H. N. Agiza, On the analysis of stability, bifurcation, chaos and chaos control of Kopel map, Chaos Solitons Fractals 10(1999), 1909-1916.
    • (1999) Chaos Solitons Fractals , vol.10 , pp. 1909-1916
    • Agiza, H.N.1
  • 3
    • 0033979874 scopus 로고    scopus 로고
    • Comparison of deterministic and stochastic SIS and SIR models in discrete time
    • L. J. S. Allen and A. B. Burgin, Comparison of deterministic and stochastic SIS and SIR models in discrete time, Math. Biosciences, 163(2000), 1-33.
    • (2000) Math. Biosciences , vol.163 , pp. 1-33
    • Allen, L.J.S.1    Burgin, A.B.2
  • 4
    • 0000755418 scopus 로고
    • Possible new strange attractors with spiral structure
    • A. Arneodo, P. Coullet, and C. Tresser, Possible new strange attractors with spiral structure, Commun. Math. Phys., 79(1981), 573-579.
    • (1981) Commun. Math. Phys , vol.79 , pp. 573-579
    • Arneodo, A.1    Coullet, P.2    Tresser, C.3
  • 6
    • 0344749621 scopus 로고
    • Mathematical analysis of a mathematical model for a plant herbivore system
    • L. J. S. Allen, M. K. Hannigan, and M. J. Strauss, Mathematical analysis of a mathematical model for a plant herbivore system, Bull. Math. Biol, 55(1993), 847-864.
    • (1993) Bull. Math. Biol , vol.55 , pp. 847-864
    • Allen, L.J.S.1    Hannigan, M.K.2    Strauss, M.J.3
  • 8
    • 0028116676 scopus 로고
    • Some discrete-time SI, SIS, and SIR epidemic models
    • L. J. S. Allen, Some discrete-time SI, SIS, and SIR epidemic models, Math. Biosciences, 124(1994), 83-105.
    • (1994) Math. Biosciences , vol.124 , pp. 83-105
    • Allen, L.J.S.1
  • 9
    • 0026336069 scopus 로고
    • A preliminary mathematical model of the apple twig borer and grapes on the Texas High Plaines
    • L. J. S. Allen, M. J. Strauss, H. G. Thorvilson, and W. N. Life, A preliminary mathematical model of the apple twig borer and grapes on the Texas High Plaines, Ecol. Model., 58(1991), 369-383.
    • (1991) Ecol. Model , vol.58 , pp. 369-383
    • Allen, L.J.S.1    Strauss, M.J.2    Thorvilson, H.G.3    Life, W.N.4
  • 11
    • 0011901580 scopus 로고    scopus 로고
    • Global first integrals for first order difference equations
    • L. Arriola, Global first integrals for first order difference equations, J. Differ. Equations Appl. 4(1998), 523-532.
    • (1998) J. Differ. Equations Appl , vol.4 , pp. 523-532
    • Arriola, L.1
  • 12
    • 0018526323 scopus 로고
    • Regular and chaotic cycling in models of ecological genetics
    • M. A. Asmussen, Regular and chaotic cycling in models of ecological genetics, Theor. Pop. Biol., 16(1979), 172-190.
    • (1979) Theor. Pop. Biol , vol.16 , pp. 172-190
    • Asmussen, M.A.1
  • 14
    • 0042115755 scopus 로고
    • Periodicity of solutions of the generalized Lyness recursion
    • E. Barbeau, B. Gelbord, and S. Tanny, Periodicity of solutions of the generalized Lyness recursion, J. Differ. Equations Appl. 1(1995), 291-306.
    • (1995) J. Differ. Equations Appl , vol.1 , pp. 291-306
    • Barbeau, E.1    Gelbord, B.2    Tanny, S.3
  • 17
    • 0001870459 scopus 로고
    • The dynamics of the Henon map
    • M. Benedicks and L. Carleson, The dynamics of the Henon map, Annals of Math. 122(1991), 73-169.
    • (1991) Annals of Math , vol.122 , pp. 73-169
    • Benedicks, M.1    Carleson, L.2
  • 18
    • 0031107120 scopus 로고    scopus 로고
    • Harvesting in discrete-time predator-prey systems
    • M. Basson and M. J. Fogarty, Harvesting in discrete-time predator-prey systems, Math. Biosciences 141(1997), 41-74.
    • (1997) Math. Biosciences , vol.141 , pp. 41-74
    • Basson, M.1    Fogarty, M.J.2
  • 19
    • 0016740371 scopus 로고
    • Dynamic complexity in predator-prey models framed in difference equations
    • J. R. Beddington, C. A. Free, and J.H. Lawton, Dynamic complexity in predator-prey models framed in difference equations, Nature, 255(1975), 58-60.
    • (1975) Nature , vol.255 , pp. 58-60
    • Beddington, J.R.1    Free, C.A.2    Lawton, J.H.3
  • 20
    • 0018174324 scopus 로고
    • Characteristics of successful natural enemies in models of biological control of insect pests
    • J. R. Beddington, C. A. Free, and J.H. Lawton, Characteristics of successful natural enemies in models of biological control of insect pests, Nature, 273(1978), 513-519.
    • (1978) Nature , vol.273 , pp. 513-519
    • Beddington, J.R.1    Free, C.A.2    Lawton, J.H.3
  • 22
    • 0001418426 scopus 로고    scopus 로고
    • Analysis of global bifurcations in a market share attraction model
    • G. I. Bischi, L. Gardini, and M. Kopel, Analysis of global bifurcations in a market share attraction model, J. Econorn. Dynamics. Control, 24(2000), 855-879.
    • (2000) J. Econorn. Dynamics. Control , vol.24 , pp. 855-879
    • Bischi, G.I.1    Gardini, L.2    Kopel, M.3
  • 23
    • 23044534920 scopus 로고    scopus 로고
    • The existence of continuous invariants for linear difference equations
    • S. Bourgault and Y. S. Huang, The existence of continuous invariants for linear difference equations, J. Differ. Equations Appl. 6(2000), 739-751.
    • (2000) J. Differ. Equations Appl , vol.6 , pp. 739-751
    • Bourgault, S.1    Huang, Y.S.2
  • 25
    • 0000776270 scopus 로고    scopus 로고
    • Multistability and cyclic attractors in duopoly games
    • G. I. Bischi, C. Mammana, and L. Gardini, Multistability and cyclic attractors in duopoly games, Chaos Solitons Fractals, 11(2000), 543-564.
    • (2000) Chaos Solitons Fractals , vol.11 , pp. 543-564
    • Bischi, G.I.1    Mammana, C.2    Gardini, L.3
  • 28
    • 21844516543 scopus 로고
    • Constant and periodic rate stocking and harvesting for Kolmogorov type population interaction models
    • J. R. Buchanan and J. F. Selgrade, Constant and periodic rate stocking and harvesting for Kolmogorov type population interaction models, Rocky Mountain J. Mathl, 25(1995), 67-85.
    • (1995) Rocky Mountain J. Mathl , vol.25 , pp. 67-85
    • Buchanan, J.R.1    Selgrade, J.F.2
  • 29
    • 0035918123 scopus 로고    scopus 로고
    • The disrete Painleve I equations: Transcendental integrability and asymptotic solutions
    • M. Bernardo, T. T. Truong, and G. Rollet, The disrete Painleve I equations: transcendental integrability and asymptotic solutions, J. Phys. A, 34(2001), 3215-3252.
    • (2001) J. Phys. A , vol.34 , pp. 3215-3252
    • Bernardo, M.1    Truong, T.T.2    Rollet, G.3
  • 30
    • 34249765954 scopus 로고
    • Stability of solutions of generalized logistic difference equations
    • W. Briden and S. Zhang, Stability of solutions of generalized logistic difference equations, Period. Math. Hung. 29(1994), 81-87.
    • (1994) Period. Math. Hung , vol.29 , pp. 81-87
    • Briden, W.1    Zhang, S.2
  • 32
    • 0000309488 scopus 로고
    • Nonlinear matrix models and population dynamics
    • J. M. Cushing, Nonlinear matrix models and population dynamics, Natural Resource Modeling, 2(1988), 539-580.
    • (1988) Natural Resource Modeling , vol.2 , pp. 539-580
    • Cushing, J.M.1
  • 34
    • 84950212619 scopus 로고
    • Second order difference equations related to the Collatz 3n + 1 conjecture
    • D. Clark, Second order difference equations related to the Collatz 3n + 1 conjecture, J. Differ. Equations Appl, 1(1985), 73-86.
    • (1985) J. Differ. Equations Appl , vol.1 , pp. 73-86
    • Clark, D.1
  • 35
    • 0008848822 scopus 로고
    • Triangulated polygons and frieze patterns
    • 175-183
    • J. H. Conway and H. S. M. Coxeter, Triangulated polygons and frieze patterns, Math. Gaz. 57(1973), 87-94 and 175-183.
    • (1973) Math. Gaz , vol.57 , pp. 87-94
    • Conway, J.H.1    Coxeter, H.S.M.2
  • 36
    • 0041738004 scopus 로고    scopus 로고
    • Multiple extinctions in a discrete competitive system
    • D. M. Chan and J. E. Franke, Multiple extinctions in a discrete competitive system, Nonlin. Anal. RWA, 2(2001), 75-91.
    • (2001) Nonlin. Anal. RWA , vol.2 , pp. 75-91
    • Chan, D.M.1    Franke, J.E.2
  • 37
    • 0017176810 scopus 로고
    • Predation in multiprey communities
    • H. N. Comins and M. P. Hassell, Predation in multiprey communities, J. Theor. Biol. 62(1976), 93-114.
    • (1976) J. Theor. Biol , vol.62 , pp. 93-114
    • Comins, H.N.1    Hassell, M.P.2
  • 38
    • 0036498930 scopus 로고    scopus 로고
    • On a coupled system of rational difference equations
    • (to appear)
    • D. Clark and M. R. S. Kulenović, On a coupled system of rational difference equations, Comp. Math. Appl. 2002 (to appear).
    • (2002) Comp. Math. Appl
    • Clark, D.1    Kulenović, M.R.S.2
  • 42
    • 0001431487 scopus 로고
    • A Collatz-type difference equation
    • D. Clark and J. T. Lewis, A Collatz-type difference equation, Congr. Numer. 111(1995), 129-135.
    • (1995) Congr. Numer , vol.111 , pp. 129-135
    • Clark, D.1    Lewis, J.T.2
  • 43
    • 33645678297 scopus 로고    scopus 로고
    • Symmetric solutions to a Collatz-like system of difference equations
    • D. Clark and J. T. Lewis, Symmetric solutions to a Collatz-like system of difference equations, Congr. Numer. 131(1998), 101-114.
    • (1998) Congr. Numer , vol.131 , pp. 101-114
    • Clark, D.1    Lewis, J.T.2
  • 46
    • 0010678168 scopus 로고
    • A piecewise linear model for the zones of instability of an area-preserving map
    • R. Devaney, A piecewise linear model for the zones of instability of an area-preserving map, Phys. D 10(1984), 387-393.
    • (1984) Phys. D , vol.10 , pp. 387-393
    • Devaney, R.1
  • 47
    • 0344156068 scopus 로고    scopus 로고
    • Fractal patterns arising in chaotic dynamical systems
    • Springer-Verlag, New York
    • M. Barnsley, R. Devaney, et al., Fractal patterns arising in chaotic dynamical systems, in The Science of Fractal Images, Springer-Verlag, New York, 1988.
    • The Science of Fractal Images , pp. 1988
    • Barnsley, M.1    Devaney, R.2
  • 48
    • 0035127368 scopus 로고    scopus 로고
    • From bi-stabilitv to chaotic oscillations in a macroeconomic model
    • R. Dieci, G. I. Bischi, and L. Gardini, From bi-stabilitv to chaotic oscillations in a macroeconomic model, Chaos Solitons Fractals, 12(2001), 805-822.
    • (2001) Chaos Solitons Fractals , vol.12 , pp. 805-822
    • Dieci, R.1    Bischi, G.I.2    Gardini, L.3
  • 49
    • 0002345071 scopus 로고
    • Global stability of a recursive sequence
    • R. DeVault, V. Kocic, and G. Ladas, Global stability of a recursive sequence, Dynam. Systems Appl, 1(1992), 13-21.
    • (1992) Dynam. Systems Appl , vol.1 , pp. 13-21
    • Devault, R.1    Kocic, V.2    Ladas, G.3
  • 51
    • 0003981716 scopus 로고    scopus 로고
    • Chapman& Hall/CRC Press. Boca Raton, FL
    • S. Elaydi, Discrete Chaos, Chapman& Hall/CRC Press. Boca Raton, FL, 2000.
    • (2000) Discrete Chaos
    • Elaydi, S.1
  • 52
    • 0039769009 scopus 로고    scopus 로고
    • A converse to Sharkovsky’s theorem
    • S. Elaydi, A converse to Sharkovsky’s theorem, Arner. Math. Month. 103(1996), 386-392.
    • (1996) Arner. Math. Month , vol.103 , pp. 386-392
    • Elaydi, S.1
  • 55
    • 84892316818 scopus 로고
    • Interactive computer simulationand analysis of Newtonian dynamics
    • S. Eubank, W. Miner, T. Tajirna, and J. Wiley. Interactive computer simulationand analysis of Newtonian dynamics, Am. J. Phys. 57 (1989), 437.
    • (1989) Am. J. Phys , vol.57 , pp. 437
    • Eubank, S.1    Miner, W.2    Tajirna, T.3    Wiley, J.4
  • 57
    • 0001816458 scopus 로고
    • Quantitative universality for a class of nonlinear transformations
    • M. J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Stat. Phys. 19(1978), 25-52.
    • (1978) J. Stat. Phys , vol.19 , pp. 25-52
    • Feigenbaum, M.J.1
  • 58
    • 0347447535 scopus 로고
    • The universal metric properties of nonlinear transformations
    • M. J. Feigenbaum, The universal metric properties of nonlinear transformations, J. Stat. Phys. 21(1979), 669-706.
    • (1979) J. Stat. Phys , vol.21 , pp. 669-706
    • Feigenbaum, M.J.1
  • 60
    • 0000533283 scopus 로고
    • Discrete Painlevé equations and their appearance in quantum gravity
    • A. S. Fokas, A. R. Its, and A. V. Kitaev, Discrete Painlevé equations and their appearance in quantum gravity, Commun. Math. Phys. 142(1991), 313-344.
    • (1991) Commun. Math. Phys , vol.142 , pp. 313-344
    • Fokas, A.S.1    Its, A.R.2    Kitaev, A.V.3
  • 61
    • 0040530623 scopus 로고    scopus 로고
    • Invariants for some rational recursive sequences with periodic coefficients
    • J. Feuer, E. Janowski, and G. Ladas, Invariants for some rational recursive sequences with periodic coefficients, J. Differ. Equations Appl. 2(1996), 167-174.
    • (1996) J. Differ. Equations Appl , vol.2 , pp. 167-174
    • Feuer, J.1    Janowski, E.2    Ladas, G.3
  • 62
    • 0000994589 scopus 로고
    • Mutual exclusion versus coexistence for discrete competitive systems
    • J. E. Franke and A-A. Yakubu, Mutual exclusion versus coexistence for discrete competitive systems, J. Math. Biol. 30(1991), 161-168.
    • (1991) J. Math. Biol , vol.30 , pp. 161-168
    • Franke, J.E.1    Yakubu, A.-A.2
  • 63
    • 0005729536 scopus 로고
    • Global attractors in competitive systems
    • J. E. Franke and A-A. Yakubu, Global attractors in competitive systems, Nonlin. Anal. TMA 16(1991), 111-129.
    • (1991) Nonlin. Anal. TMA , vol.16 , pp. 111-129
    • Franke, J.E.1    Yakubu, A.-A.2
  • 64
    • 38249007755 scopus 로고
    • Geometry of exclusion principles in discrete systems
    • J. E. Franke and A-A. Yakubu, Geometry of exclusion principles in discrete systems, J. Math. Anal. Appl. 168(1992), 385-400.
    • (1992) J. Math. Anal. Appl , vol.168 , pp. 385-400
    • Franke, J.E.1    Yakubu, A.-A.2
  • 73
    • 0002591468 scopus 로고
    • A two dimensional mapping with a strange attractor
    • M. Henon, A two dimensional mapping with a strange attractor, Comm. Math. Phys., 50(1976), 69-77.
    • (1976) Comm. Math. Phys , vol.50 , pp. 69-77
    • Henon, M.1
  • 75
    • 0030286119 scopus 로고    scopus 로고
    • K-integrals and £-Lie symmetries in discrete dynamical systems
    • F. A. Haggar, G. B. Byrnes, G. R. W. Quispel, and H. W. Capel, k-integrals and £-Lie symmetries in discrete dynamical systems. Physica A 233(1996), 379-394.
    • (1996) Physica A , vol.233 , pp. 379-394
    • Haggar, F.A.1    Byrnes, G.B.2    Quispel, G.R.W.3    Capel, H.W.4
  • 76
    • 0016947226 scopus 로고
    • Discrete time models for two-species competition
    • M. P. Hassell and H. N. Cornins, Discrete time models for two-species competition, Theor. Pop. Biol. 9(1976), 202-221.
    • (1976) Theor. Pop. Biol , vol.9 , pp. 202-221
    • Hassell, M.P.1    Cornins, H.N.2
  • 77
    • 0026268962 scopus 로고
    • Spatial structure and chaos in insect population dynamics
    • M. P. Hassell, H. N. Cornins, and R. M. May, Spatial structure and chaos in insect population dynamics, Nature 353(1991), 255-258.
    • (1991) Nature , vol.353 , pp. 255-258
    • Hassell, M.P.1    Cornins, H.N.2    May, R.M.3
  • 78
    • 84880026161 scopus 로고
    • Some characteristics of simple types of predation and parasitism
    • C. S. Holling, Some characteristics of simple types of predation and parasitism, Can. Ent. 91(1959), 385-398.
    • (1959) Can. Ent , vol.91 , pp. 385-398
    • Holling, C.S.1
  • 79
    • 0003421845 scopus 로고
    • Springer-Verlag, New York, Berlin, Heidelberg, Tokyo
    • J. Hale and H. Kocak, Dynamics and Bifurcations, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1991.
    • (1991) Dynamics and Bifurcations
    • Hale, J.1    Kocak, H.2
  • 80
    • 0000289792 scopus 로고
    • Stability in insect host-parasite models
    • M. P. Hassell and R. M. May, Stability in insect host-parasite models, J. Anim. Ecol. 42(1973), 693-726.
    • (1973) J. Anim. Ecol , vol.42 , pp. 693-726
    • Hassell, M.P.1    May, R.M.2
  • 81
    • 0010670394 scopus 로고    scopus 로고
    • Phase portraits for a class of difference equations
    • Phase portraits for a class of difference equations, J. Differ. Equations Appl. 5(1999), 177-202.
    • (1999) J. Differ. Equations Appl , vol.5 , pp. 177-202
  • 84
    • 0001265433 scopus 로고
    • Fractals and self-similarity
    • J. Hutchinson, Fractals and self-similarity, Indiana Univ. J. Math,., 30(1981), 713-747.
    • (1981) Indiana Univ. J. Math , vol.30 , pp. 713-747
    • Hutchinson, J.1
  • 86
    • 0038373122 scopus 로고
    • Singularity analysis and integrability for disrete dynamical systems
    • N. Joshi, Singularity analysis and integrability for disrete dynamical systems, J. Math. Anal. Appl, 184(1994), 573-584.
    • (1994) J. Math. Anal. Appl , vol.184 , pp. 573-584
    • Joshi, N.1
  • 89
    • 0011167827 scopus 로고
    • Modelling populations of cyst-nematodes (Nematoda: Heteroderidae)
    • F. Jones and J. Perry, Modelling populations of cyst-nematodes (nematoda: heteroderidae), J. Appl. Ecology, 15(1978), 349-371.
    • (1978) J. Appl. Ecology , vol.15 , pp. 349-371
    • Jones, F.1    Perry, J.2
  • 90
    • 0023487191 scopus 로고
    • The discrete dynamics of symmetric competition in the plane
    • H. Jiang and T. D. Rogers, The discrete dynamics of symmetric competition in the plane, J. Math. Biol. 25(1987), 573-596.
    • (1987) J. Math. Biol , vol.25 , pp. 573-596
    • Jiang, H.1    Rogers, T.D.2
  • 92
    • 0001614195 scopus 로고
    • Sur une corbe continué sans tangente, obtenue par une construction géometrique élémentaire
    • H. von Koch, Sur une corbe continué sans tangente, obtenue par une construction géometrique élémentaire, Arkiv fur Mathematik 1(1904), 681-704.
    • (1904) Arkiv Fur Mathematik , vol.1 , pp. 681-704
    • Von Koch, H.1
  • 93
    • 0030512941 scopus 로고    scopus 로고
    • Complex non-unique dynamics in ecological interactions
    • V. Kaitala and M. Heino, Complex non-unique dynamics in ecological interactions, Proc. R. Soc. London B 263(1996), 1011-1013.
    • (1996) Proc. R. Soc. London B , vol.263 , pp. 1011-1013
    • Kaitala, V.1    Heino, M.2
  • 94
    • 0031149367 scopus 로고    scopus 로고
    • Host-parasite dynamics and the evolution of host immunity and parasite fecundity strategies
    • V. Kaitala, M. Heino, and W Getz, Host-parasite dynamics and the evolution of host immunity and parasite fecundity strategies, Bull. Math. Biol. 59(1997), 427-450.
    • (1997) Bull. Math. Biol , vol.59 , pp. 427-450
    • Kaitala, V.1    Heino, M.2    Getz, W.3
  • 99
    • 0023635696 scopus 로고
    • Linearized oscillations in population dynamics
    • M.R.S. Kulenović and G. Ladas, Linearized oscillations in population dynamics, Bull. Math. Biol. 49 (5) (1987), 615-627.
    • (1987) Bull. Math. Biol , vol.49 , Issue.5 , pp. 615-627
    • Kulenovi, M.R.S.1    Ćladas, G.2
  • 102
    • 0034831844 scopus 로고    scopus 로고
    • On a rational difference equation, Cornput
    • M. R. S. Kulenović, G. Ladas, and N. R. Prokup, On a rational difference equation, Cornput. Math. Appl. 41(2001), 671-678.
    • (2001) Math. Appl , vol.41 , pp. 671-678
    • Kulenovi, M.R.S.1    Ćladas, G.2    Prokup, N.R.3
  • 107
    • 85057456597 scopus 로고    scopus 로고
    • Global asymptotic behavior of a two dimensional system of difference equations modelling cooperation
    • to appear
    • M. R. S. Kulenović and M. Nurkanović, Global asymptotic behavior of a two dimensional system of difference equations modelling cooperation, J. Differ. Equations Appl. 8(2002), to appear.
    • (2002) J. Differ. Equations Appl , vol.8
    • Kulenovi, M.R.S.1    Ćnurkanović, M.2
  • 108
    • 0001014896 scopus 로고    scopus 로고
    • Simple and complex adjusment dynamics in Cournot Duopoly model
    • M. Kopel, Simple and complex adjusment dynamics in Cournot Duopoly model, Chaos Solitons Fractals 7(1996), 2031-2048.
    • (1996) Chaos Solitons Fractals , vol.7 , pp. 2031-2048
    • Kopel, M.1
  • 111
    • 0346171074 scopus 로고
    • Perfect harmony: The discrete dynamics of cooperation
    • W. Krawcewicz and T. D. Rogers, Perfect harmony: the discrete dynamics of cooperation, J. Math. Biol. 28(1990), 383-410.
    • (1990) J. Math. Biol , vol.28 , pp. 383-410
    • Krawcewicz, W.1    Rogers, T.D.2
  • 112
    • 0010713798 scopus 로고    scopus 로고
    • Invariants and related Liapunov functions for difference equations, Appl
    • M. R. S. Kulenović, Invariants and related Liapunov functions for difference equations, Appl. Math. Lett. 13(2000), 1-8.
    • (2000) Math. Lett , vol.13 , pp. 1-8
    • Kulenović, M.R.S.1
  • 113
    • 0001277608 scopus 로고
    • Local structure of turbulence in an incompressible liquid for very large Reynolds numbers
    • A. N. Kolmogorov, Local structure of turbulence in an incompressible liquid for very large Reynolds numbers, C. R. Acad. Sci. USSR 30(1941), 299-303.
    • (1941) C. R. Acad. Sci. USSR , vol.30 , pp. 299-303
    • Kolmogorov, A.N.1
  • 114
    • 0034610197 scopus 로고    scopus 로고
    • Non-unique population dynamics: Basic patterns, Ecol
    • V. Kaitala, J. Ylikarjula, and M. Heino, Non-unique population dynamics: basic patterns, Ecol. Modelling 135(2000), 127-134.
    • (2000) Modelling , vol.135 , pp. 127-134
    • Kaitala, V.1    Ylikarjula, J.2    Heino, M.3
  • 118
    • 0013218207 scopus 로고
    • Princeton University Press, Princeton
    • H. Lauwerier, Fractals, Princeton University Press, Princeton, 1991.
    • (1991) Fractals
    • Lauwerier, H.1
  • 119
    • 85057479728 scopus 로고
    • Chaos, A. V. Holden, Ed., Manchester Univ. Press, Manchester
    • H. A. Lauwerier, One-dimensional iterative maps, in Chaos, A. V. Holden, Ed., Manchester Univ. Press, Manchester, 1986, 39-57.
    • (1986) One-Dimensional Iterative Maps , pp. 39-57
    • Lauwerier, H.A.1
  • 120
    • 0003291236 scopus 로고
    • Chaos, A. V. Holden, Ed., Manchester Univ. Press, Manchester
    • H. A. Lauwerier, Two-dimensional iterative maps, in Chaos, A. V. Holden, Ed., Manchester Univ. Press, Manchester, 1986, 58-97.
    • (1986) Two-Dimensional Iterative Maps , pp. 58-97
    • Lauwerier, H.A.1
  • 121
    • 0002747273 scopus 로고
    • The 3x+ 1 problem and its generalizations
    • J. C. Lagarias, The 3x+ 1 problem and its generalizations, Arner. Math. Monthly 92(1985), 3-23.
    • (1985) Arner. Math. Monthly , vol.92 , pp. 3-23
    • Lagarias, J.C.1
  • 122
    • 84963444270 scopus 로고
    • Invariants for generalized Lyness equations
    • G. Ladas, Invariants for generalized Lyness equations, J. Differ. Equations Appl. 1(1995), 209-214.
    • (1995) J. Differ. Equations Appl , vol.1 , pp. 209-214
    • Ladas, G.1
  • 127
    • 0000100336 scopus 로고
    • Period three implies chaos
    • T. Y. Li and J. A. Yorke, Period three implies chaos, Amer. Math. Monthly 82(1975), 985-992.
    • (1975) Amer. Math. Monthly , vol.82 , pp. 985-992
    • Li, T.Y.1    Yorke, J.A.2
  • 129
    • 0016394337 scopus 로고
    • Biological populations with nonoverlapping generations: Stable points, stable cycles and chaos
    • R. M. May, Biological populations with nonoverlapping generations: stable points, stable cycles and chaos, Science 186(1974), 645-647.
    • (1974) Science , vol.186 , pp. 645-647
    • May, R.M.1
  • 130
    • 0000487177 scopus 로고
    • Host-parasitoid systems in patchy environments: A phenomenological model
    • R. M. May, Host-parasitoid systems in patchy environments: a phenomenological model, J. Animal Ecol. 47(1978), 833-843.
    • (1978) J. Animal Ecol , vol.47 , pp. 833-843
    • May, R.M.1
  • 131
    • 0001714305 scopus 로고
    • The dynamics of multiparasitoid-host interactions
    • R. M. May and M. P. Hassell, The dynamics of multiparasitoid-host interactions, The American Naturalist 117(1981), 234-261.
    • (1981) The American Naturalist , vol.117 , pp. 234-261
    • May, R.M.1    Hassell, M.P.2
  • 132
    • 0038957699 scopus 로고
    • The similarity method for difference equations
    • S. Maeda, The similarity method for difference equations, IMA J. Appl. Math. 38(1987), 129-134.
    • (1987) IMA J. Appl. Math , vol.38 , pp. 129-134
    • Maeda, S.1
  • 134
    • 0003805342 scopus 로고
    • World Scientific, Singapore
    • C. Mira, Chaotic Dynamics, World Scientific, Singapore, 1987.
    • (1987) Chaotic Dynamics
    • Mira, C.1
  • 136
    • 0000017280 scopus 로고
    • Some remarks on animal population dynamics
    • P. A. B. Moran, Some remarks on animal population dynamics, Biometrics 6(1950), 250-258.
    • (1950) Biometrics , vol.6 , pp. 250-258
    • Moran, P.A.B.1
  • 137
    • 0003588811 scopus 로고
    • Stable and Random Motions in Dynamical Systems, Princeton University Press
    • J. Moser, Stable and Random Motions in Dynamical Systems, Princeton University Press, Princeton, 1973.
    • (1973) Princeton
    • Moser, J.1
  • 139
    • 0004486521 scopus 로고
    • St, range limits of stability in host-parasitoid systems
    • C. Meier, W. Senn, R. Hauser, and M. Zimmermann, St, range limits of stability in host-parasitoid systems, J. Math. Biol, 32(1994), 563-572.
    • (1994) J. Math. Biol , vol.32 , pp. 563-572
    • Meier, C.1    Senn, W.2    Hauser, R.3    Zimmermann, M.4
  • 142
    • 0039823376 scopus 로고
    • Iteration der reellen polynonie zweiten grades
    • P. J. Myrberg, Iteration der reellen polynonie zweiten grades, I Ann. Acad. Sci. Fennicae 256(1958). 1-10.
    • (1958) I Ann. Acad. Sci. Fennicae , vol.256 , pp. 1-10
    • Myrberg, P.J.1
  • 143
    • 0010829632 scopus 로고
    • Iteration der reellen polynonie zweiten grades
    • P. J. Myrberg, Iteration der reellen polynonie zweiten grades, II Ann. Acad. Sci. Fennicae 268(1959). 1-18.
    • (1959) II Ann. Acad. Sci. Fennicae , vol.268 , pp. 1-18
    • Myrberg, P.J.1
  • 144
    • 0010829632 scopus 로고
    • Iteration der reellen polynonie zweiten grades
    • P. J. Myrberg, Iteration der reellen polynonie zweiten grades, III Ann. Acad. Sci. Fennicae 336(1963). 1-10.
    • (1963) III Ann. Acad. Sci. Fennicae , vol.336 , pp. 1-10
    • Myrberg, P.J.1
  • 145
    • 0010219788 scopus 로고
    • Sur Titration des polynoines rels quadratiques
    • P. J. Myrberg, Sur Titration des polynoines rels quadratiques, J. Math. Pures Appl. (9) 41 (1962), 339-351.
    • (1962) J. Math. Pures Appl , vol.41 , Issue.9 , pp. 339-351
    • Myrberg, P.J.1
  • 146
    • 12844280488 scopus 로고
    • Introducing students to non-linearity: Computer experiments with with Burgers mappings
    • N. MacDonald and R. R. Whitehead, Introducing students to non-linearity: Computer experiments with with Burgers mappings, Eur. J. Phys. 6(1985), 143.
    • (1985) Eur. J. Phys , vol.6 , pp. 143
    • Macdonald, N.1    Whitehead, R.R.2
  • 148
    • 0004234755 scopus 로고    scopus 로고
    • second edition, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo
    • H. Nusse and J. A. Yorke, Dynamics: Numerical Explorations, second edition, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1998.
    • (1998) Dynamics: Numerical Explorations
    • Nusse, H.1    Yorke, J.A.2
  • 150
    • 0002267817 scopus 로고
    • An open-access analysis of the northern anchovy fishery
    • J. D. Opsomer and J. M. Conrad, An open-access analysis of the northern anchovy fishery, J. Environ. Econ. Manag. 27(1994), 21-37.
    • (1994) J. Environ. Econ. Manag , vol.27 , pp. 21-37
    • Opsomer, J.D.1    Conrad, J.M.2
  • 152
    • 0010057547 scopus 로고
    • Chaos in duopoly pricing
    • T. Puu, Chaos in duopoly pricing, Chaos Solitons Fractals 1(1991), 573-581.
    • (1991) Chaos Solitons Fractals , vol.1 , pp. 573-581
    • Puu, T.1
  • 153
    • 0032517943 scopus 로고    scopus 로고
    • The chaotic duopolists revisited
    • T. Puu, The chaotic duopolists revisited, J. Econom. Behavior & Organization 33(1998), 385-394.
    • (1998) J. Econom. Behavior & Organization , vol.33 , pp. 385-394
    • Puu, T.1
  • 155
    • 0013017548 scopus 로고    scopus 로고
    • Stability of a class of nonlinear difference equations
    • G. Papaschinopoulos and C. J. Schinas, Stability of a class of nonlinear difference equations, J. Math. Anal. Appl., 230(1999), 211-222.
    • (1999) J. Math. Anal. Appl , vol.230 , pp. 211-222
    • Papaschinopoulos, G.1    Schinas, C.J.2
  • 156
    • 85057451585 scopus 로고    scopus 로고
    • Generalized invariants for systems of difference equations of rational form
    • G. Papaschinopoulos and C. J. Schinas, Generalized invariants for systems of difference equations of rational form. Neural Parallel Sci. Comput. 7(1999), 379-404.
    • (1999) Neural Parallel Sci. Comput , vol.7 , pp. 379-404
    • Papaschinopoulos, G.1    Schinas, C.J.2
  • 159
    • 45149143692 scopus 로고
    • Inte-grable mappings and soliton equations II
    • G. R. W. Quispel, J. A. G. Roberts, and C. J. Thompson, Inte-grable mappings and soliton equations II, Physica D 34 (1989), 183-192.
    • (1989) Physica D , vol.34 , pp. 183-192
    • Quispel, G.R.W.1    Roberts, J.A.G.2    Thompson, C.J.3
  • 160
    • 4243673219 scopus 로고
    • Lie symmetries and integration of difference equations
    • G. R. W. Quispel and R. Sahadevan, Lie symmetries and integration of difference equations, Phys. Lett. A 184 (1993), 64-70.
    • (1993) Phys. Lett. A , vol.184 , pp. 64-70
    • Quispel, G.R.W.1    Sahadevan, R.2
  • 162
    • 0000374060 scopus 로고
    • Exotic phenomena in games and duopoly models
    • D. Rand, Exotic phenomena in games and duopoly models, J. Math. Econ. 5(1978), 173-184.
    • (1978) J. Math. Econ , vol.5 , pp. 173-184
    • Rand, D.1
  • 163
    • 0000722180 scopus 로고
    • Stock and recruitment
    • W. E. Ricker, Stock and recruitment, J. Fish. Res. Dd. Can. 11(1954), 559-623.
    • (1954) J. Fish. Res. Dd. Can , vol.11 , pp. 559-623
    • Ricker, W.E.1
  • 164
    • 0002992365 scopus 로고
    • Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems
    • J. A. G. Roberts and G. R. W. Quispel, Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems, Phys. Rep. 216(1992), 53-117.
    • (1992) Phys. Rep , vol.216 , pp. 53-117
    • Roberts, J.A.G.1    Quispel, G.R.W.2
  • 165
    • 0000971991 scopus 로고
    • Random search and insect population models
    • D. J. Rogers, Random search and insect population models, J. Anim. Ecol. 41(1972), 369-383.
    • (1972) J. Anim. Ecol , vol.41 , pp. 369-383
    • Rogers, D.J.1
  • 166
    • 51649171552 scopus 로고
    • A comparative study of models for predation and parasitism
    • T. Royama, A comparative study of models for predation and parasitism, Res. Popul. Biol. Ecol. (1971), 1-91.
    • (1971) Res. Popul. Biol. Ecol , pp. 1-91
    • Royama, T.1
  • 168
    • 0000152674 scopus 로고    scopus 로고
    • Planar competitive and cooperative difference equations
    • H. L. Smith, Planar competitive and cooperative difference equations, J. Differ. Equations Appl, 3(1998), 335-357.
    • (1998) J. Differ. Equations Appl , vol.3 , pp. 335-357
    • Smith, H.L.1
  • 170
    • 0031195382 scopus 로고    scopus 로고
    • Invariants for some difference equations
    • C. J. Schinas, Invariants for some difference equations, J. Math. Anal. Appl., 212(1997), 281-291.
    • (1997) J. Math. Anal. Appl , vol.212 , pp. 281-291
    • Schinas, C.J.1
  • 171
    • 0031284334 scopus 로고    scopus 로고
    • Invariants for difference equations and systems of difference equations of rational form
    • C. J. Schinas, Invariants for difference equations and systems of difference equations of rational form, J. Math. Anal. Appl., 216(1997), 164-179.
    • (1997) J. Math. Anal. Appl , vol.216 , pp. 164-179
    • Schinas, C.J.1
  • 172
    • 0010668338 scopus 로고    scopus 로고
    • Using stocking or harvesting to reverse period-doubling bifurcations in discrete population models
    • J. F. Selgrade, Using stocking or harvesting to reverse period-doubling bifurcations in discrete population models, J. Differ. Equations Appl, 4(1998), 163-183.
    • (1998) J. Differ. Equations Appl , vol.4 , pp. 163-183
    • Selgrade, J.F.1
  • 174
    • 0002072428 scopus 로고
    • Co-existence of cycles of a continuous mapping of a line into itself, Ukranian
    • A. N. Sharkovsky, Co-existence of cycles of a continuous mapping of a line into itself, Ukranian Math. Z. 16(1964), 61-71.
    • (1964) Math. Z , vol.16 , pp. 61-71
    • Sharkovsky, A.N.1
  • 175
    • 0001273984 scopus 로고
    • Stable orbits and bifurcation of maps of the interval
    • D. Singer, Stable orbits and bifurcation of maps of the interval, SIAM J. Appl. Math,., 35(1978), 260-267.
    • (1978) SIAM J. Appl. Math , vol.35 , pp. 260-267
    • Singer, D.1
  • 176
    • 0036000437 scopus 로고    scopus 로고
    • Periodicity of recursive sequances and the dynamics of homogeneous piecewise linear maps of the plane
    • to appear
    • A. G. Sivak, Periodicity of recursive sequances and the dynamics of homogeneous piecewise linear maps of the plane, J. Differ. Equations Appl., 8(2002), to appear.
    • (2002) J. Differ. Equations Appl , vol.8
    • Sivak, A.G.1
  • 180
    • 0025591756 scopus 로고
    • Stable periodic behavior in a pioneer-climax model
    • J. F. Selgrade and G. Namkoong, Stable periodic behavior in a pioneer-climax model, Nat. Resource Model., 4(1990), 215-227.
    • (1990) Nat. Resource Model , vol.4 , pp. 215-227
    • Selgrade, J.F.1    Namkoong, G.2
  • 181
    • 0011812535 scopus 로고
    • Population interactions with growth rates dependent on weighted densities, Differential Equations in Models in Biology, Epidemiology and Ecology
    • S. Busen-berg and M. Martelli, eds, Springer-Verlag, Berlin
    • J. F. Selgrade and G. Namkoong, Population interactions with growth rates dependent on weighted densities, Differential Equations in Models in Biology, Epidemiology and Ecology, S. Busen-berg and M. Martelli, eds., Lect. Notes in Biomath. 92, Springer-Verlag, Berlin, 1991, 247-256.
    • (1991) Lect. Notes in Biomath. 92 , pp. 247-256
    • Selgrade, J.F.1    Namkoong, G.2
  • 182
    • 0030736791 scopus 로고    scopus 로고
    • Lie symmetries and linearisation of the QRT mapping
    • R. Sahadevan and G. R. W. Quispel, Lie symmetries and linearisation of the QRT mapping, Physica A(1997) 234, 775-784.
    • (1997) Physica A , vol.234 , pp. 775-784
    • Sahadevan, R.1    Quispel, G.R.W.2
  • 183
    • 0029659922 scopus 로고    scopus 로고
    • Lumped-density population models of pioneer-climax type and stability analysis of Hopf bifurcations
    • J. F. Selgrade and J. H. Roberds, Lumped-density population models of pioneer-climax type and stability analysis of Hopf bifurcations, Math. Biosciences 135(1996), 1-21.
    • (1996) Math. Biosciences , vol.135 , pp. 1-21
    • Selgrade, J.F.1    Roberds, J.H.2
  • 184
    • 0031186672 scopus 로고    scopus 로고
    • Period-doubling bifurcations for systems of difference equations and applications to models in population biology
    • J. F. Selgrade and J. H. Roberds, Period-doubling bifurcations for systems of difference equations and applications to models in population biology, Nonlin. Anal. TMA 29(1997), 185-199.
    • (1997) Nonlin. Anal. TMA , vol.29 , pp. 185-199
    • Selgrade, J.F.1    Roberds, J.H.2
  • 185
    • 0023477339 scopus 로고
    • Convergence to equilibrium in a genetic model with differential viability between the sexes
    • J. F. Selgrade and M. Ziehe, Convergence to equilibrium in a genetic model with differential viability between the sexes, J. Math. Biol., 25(1987), 477-490.
    • (1987) J. Math. Biol , vol.25 , pp. 477-490
    • Selgrade, J.F.1    Ziehe, M.2
  • 186
    • 0013642372 scopus 로고
    • Aggregation, competition, and host-parasitoid dynamics: Stability conditions don’t tell it all
    • A. D. Taylor, Aggregation, competition, and host-parasitoid dynamics: stability conditions don’t tell it all, The American Naturalist 141(1993), 501-506.
    • (1993) The American Naturalist , vol.141 , pp. 501-506
    • Taylor, A.D.1
  • 187
    • 23044533749 scopus 로고    scopus 로고
    • A note of the theoretical existence of invariants: Part I
    • E. S. Thomas and S. Bourgault, A note of the theoretical existence of invariants: part I, J. Differ. Equations Appl. 6(2000), 681-693.
    • (2000) J. Differ. Equations Appl , vol.6 , pp. 681-693
    • Thomas, E.S.1    Bourgault, S.2
  • 189
    • 21344492385 scopus 로고
    • On intervals: Transitivity → chaos
    • M. Vellekop and R. Berglund, On intervals: Transitivity → chaos, Am. Math. Month. 101(1994), 353-355.
    • (1994) Am. Math. Month , vol.101 , pp. 353-355
    • Vellekop, M.1    Berglund, R.2
  • 192
    • 0033102348 scopus 로고    scopus 로고
    • Global stability of discrete models of Lotka-Volterra type
    • W. Wang and L. Zhengyi, Global stability of discrete models of Lotka-Volterra type, Nonlin. Anal. TMA 35(1999), 1019-1030.
    • (1999) Nonlin. Anal. TMA , vol.35 , pp. 1019-1030
    • Wang, W.1    Zhengyi, L.2
  • 193
    • 0028985509 scopus 로고
    • The effect of planting and harvesting on endangered species in discrete competitive systems
    • A-A. Yakubu, The effect of planting and harvesting on endangered species in discrete competitive systems, Math. Biosci. 126(1995), 1-20.
    • (1995) Math. Biosci , vol.126 , pp. 1-20
    • Yakubu, A.-A.1
  • 194
    • 0001415921 scopus 로고    scopus 로고
    • A discrete competitive system with planting
    • A-A. Yakubu, A discrete competitive system with planting, J. Differ. Equations Appl, 4(1998), 213-214.
    • (1998) J. Differ. Equations Appl , vol.4 , pp. 213-214
    • Yakubu, A.-A.1


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