Bifurcations and chaotic dynamics in a 4-dimensional competitive Lotka–Volterra system
Bifurcations and chaotic dynamics in a 4-dimensional competitive Lotka–Volterra system
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DOI：
10.1007/s11071-009-9547-3
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发表时间：
2010-02
影响因子：
5.6
通讯作者：
Ruiping. Wang;Dongmei Xiao
中科院分区：
文献类型：
--
作者：
Ruiping. Wang;Dongmei Xiao
本文研究了四维竞争Lotka-Volterra系统的Hopf分支，并给出了一个类似于Rössler折叠带吸引子的混沌动力学例子。这证明了斯梅尔在(J.)Math.Biol.，3：5-7,1976)，即使对于最简单的竞争Lotka-Volterra系统，当维度为4时也成立。探讨了四维竞争Lotka-Volterra系统混沌行为的发生机制。数值研究表明，由Hopf分支得到的周期解可以经历连续倍周期级联，而由Shil‘nikov定理得到的同宿轨道可以经历同宿分支。
In this paper, we study the Hopf bifurcation for the four-dimensional competitive Lotka–Volterra system, and give an example which can display chaotic dynamics apparent like Rössler’s folded band attractor. This demonstrates that Smale’s conclusions in (J. Math. Biol., 3:5–7, 1976) are true even for the simplest competitive Lotka–Volterra systems when the dimensionnis four. We explore the mechanism of occurrence of chaotic behavior for the four-dimensional competitive Lotka–Volterra system. The numerical study indicates that a periodic solution by Hopf bifurcation can undergo successive period-doubling cascades, and a homoclinic orbit can undergo homoclinic bifurcation by Shil’nikov theorem.