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Dynamical Behaviors in a Two-dimensional Map 被引量：1

Dynamical Behaviors in a Two-dimensional Map
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摘要 We consider the dynamics of a two-dimensional map proposed by Maynard Smith as a population model. The existence of chaos in the sense of Marotto's theorem is first proved, and the bifurcations of periodic points are studied by analytic methods. The numerical simulations not only show the consistence with the theoretical analysis but also exhibi the complex dynamical behaviors.
作者 YuChang Xu-dongLi
机构地区 BeijingRemoteSensingInstitute InstituteofAppliedPhysicsandComputationalMathematics
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2003年第4期663-676,共14页 应用数学学报（英文版）
基金 Supported by Chinese Academy Sciences (KZCX2-SW-118).
关键词 Snap-back repellers CHAOS Hopf bifurcation strong (weak) resonance Snap-back repellers chaos Hopf bifurcation strong (weak) resonance
分类号 C92 [社会学—人口学] O241.8 [理学—计算数学]
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参考文献14

  • 1David Whitley. Discrete dynamical Systems in dimensions one and two. Bull. London Math. Soc., 15:177-217 (1983).
  • 2David whitley. On the periodic points of a two-parameter family of maps of the plane. Acta. Appl.Math., 5:279-311 (1986).
  • 3Guckenheimer, J., Holemes, P.J. Nonlinear oscillations, dynamical systems and bifurcations of vector fields.Springer-Verlag, New York, 1983.
  • 4Iooss, G. Bifurcation of maps and applications. North-Holland, Amsterdan 1977.
  • 5Jiang, H., Rogers, T.D. The discrete dynamics of symmetric competition in the plane, J. Math. Biol., 25:573-596 (1987).
  • 6Li, T.Y. Yorke, J.A. Period three implies chaos. Amer. Math. Monthly, 82:985-992 (1975).
  • 7Marotto,F.R.Snap-back repellers imply chaos in R^n.J.Math.Anal.and Appl.,63:199-223(1978)
  • 8May,R.Biological populations with non-overlapping generations:stable points,stable cycles and chaos.Science,186:645-647(1974)
  • 9May, R. Biological populations obeying difference equations: stable points, periodic orbits and chaos. J.Theoret. Biol., 51:511-524 (1975).
  • 10May, R., Oster, G. Bifurcations and dynamical stability in simple ecological models. Am. Naturalist., 110:573-599 (1976).

同被引文献6

  • 1Smith M J. Mathematical ideas in biology[M]. Cambridge: Cambridge University Press, 1968.35-47.
  • 2Tang S Y, Chen L S. Chaos in functional response host-parasitoid ecosystem models[J]. Chaos, Solitons and Fractals, 2002,13:875-884.
  • 3Parker T S, Chua L O. Practical numerical algorithms for chaotic systems[M]. New York: Springer, 1989.66-71.
  • 4Rasband S N. Chaotic dynamics of nonlinear system[M]. New York: Wiley/Interscience, 1990.187-195.
  • 5Isidori A. Nonlinear control systems[M]. 3rd ed. New York: Springer, 1995.137-218.
  • 6赵立纯,张庆灵,杨启昌.具有周期系数的单种群模型的最优脉冲控制[J].东北大学学报（自然科学版）,2002,23(11):1040-1043. 被引量：4

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Acta Mathematicae Applicatae Sinica
2003年 第4期

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