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三种群Lotka-Volterra捕食系统多个极限环的存在性 被引量：2

A Three Species Lotka-Volterra Prey-Predator System with Multiple Limit Cycles
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摘要 通过降维把高维系统平衡点的稳定性及极限环的构造用低维系统来判定和实现,给出了一个三种群Lotka-Volterra捕食系统具有两个小扰动极限环的例子。 Based on the Center Manifold Theorem and the Liapunov method, an example of a three species Lotka-V'olferra prey-predator system with two samll amplitude limit cycles is constructed.
作者 罗勇 陆征一
机构地区 四川大学数学学院 温州师范学院系统科学研究所
出处 《生物数学学报》 CSCD 2002年第3期293-298,共6页 Journal of Biomathematics
基金 国家重点基础研究发展规划资助项目(G1998030600)
关键词 Lotka-Volterra捕食系统 极限环 存在性 中心流形 Lotka-Volterra system Prey-Predator Center mamfold Limit cycles
分类号 Q141 [生物学—生态学]
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参考文献9

  • 1Cart J. Applications of Center Manifold Theory[M]. New York: Springer-Verlag, 1981.
  • 2Coste J, Peyraud J, Coullet P. Asymptotic behaviour in the dynamics of competing species[J]. SIAM J Appl Math. 1979, 36. 516-542.
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  • 4Hofbauer J. On the occurrence of limit cycles in the Volterra-Lotka equation[J]. Nonlinear Analysis, 1981.5:1003-1007.
  • 5Hofbauer J, So J W. Multiple limit cycles for three dimensional Lotka-Volterra equationsp[J]. Appl Math Lett, 1994, 7:65-70.
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  • 8Xiao D, Li W. Limit cycles for the competitive three dinensional Lotka-Volterra system[J]. J Diff Eqns.2000, 164:1-15.
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同被引文献34

  • 1刘立,陆征一,王东明.THE STRUCTURE OF LASALLE’S INVARIANT SET FOR LOTKA-VOLTERRA SYSTEMS[J].Science China Mathematics,1991,34(7):783-790. 被引量：4
  • 2Volterra V. Variations and Fluctuations in the Numbers of Coexisting Animal Species. Berlin: Springer-Verlag, 1928.
  • 3Lotka A J. Undamped oscillations derived from the law of mass action. J. Am. Chem. Soc., 1920, 42: 1595-1598.
  • 4Scudo F and Ziegler J. The Golden Age of Theoretical Ecology. New York, Springer, 1978.
  • 5Peschel M, Mende W. The Predator-Prey Models. New York: Springer, 1986.
  • 6Hofbauer J and Sigmund K. Evolution Games and Population Dynamical Systems. Cambridge University Press, Cambridge, 1998.
  • 7Bomze I M. Lotka-Volterra equation and replicator dynamics: New issues in classification. Biol. Cybern., 1995, 72: 447-453.
  • 8Bomze I M. Lotka-Volterra equations and replicator dynamics: A two dimensional classification. Biol. Cybern., 1983, 48: 201-211.
  • 9Jansen W. A permanence theorem for replicator and Lotka-Volterra systems. J. Math. Biol., 1987, 25: 411-422.
  • 10Butler G and Waltman P. Persistence in dynamical systems. J. Diff. Eqns., 1986, 63: 255-263.

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二级引证文献4

生物数学学报
2002年 第3期

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