Bifurcation Analysis in an n-Dimensional Diffusive Competitive Lotka-Volterra System with Time Delay
Bifurcation Analysis in an n-Dimensional Diffusive Competitive Lotka-Volterra System with Time Delay
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DOI：
10.1142/s0218127415500893
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
Xiaoyuan Chang;Junjie Wei
中科院分区：
文献类型：
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作者：
Xiaoyuan Chang;Junjie Wei
本文研究了一类具有齐次Dirichlet边界条件的时滞n维竞争Lotka-Volterra扩散系统的稳定性和Hopf分支。我们首先证明了存在满足给定渐近表达式的非恒定正定态解，并证明了该非恒定正解的稳定性。将时滞作为分叉参数，研究了在非恒定定态正解附近发生Hopf分叉的系统，给出了确定Hopf分叉方向的计算方法。最后，我们引用三维时滞竞争Lotka-Volterra扩散系统的稳定性来说明我们的结论。
In this paper, we investigate the stability and Hopf bifurcation of an n-dimensional competitive Lotka–Volterra diffusion system with time delay and homogeneous Dirichlet boundary condition. We first show that there exists a positive nonconstant steady state solution satisfying the given asymptotic expressions and establish the stability of the positive nonconstant steady state solution. Regarding the time delay as a bifurcation parameter, we explore the system that undergoes a Hopf bifurcation near the positive nonconstant steady state solution and derive a calculation method for determining the direction of the Hopf bifurcation. Finally, we cite the stability of a three-dimensional competitive Lotka–Volterra diffusion system with time delay to illustrate our conclusions.