具有时滞分段常数变量与干扰比率模型的分支分析

Bifurcation analysis of the model with time-delay,piecewise constant variables and interference

为讨论具有时滞、干扰和分段常数变量的单种群比率密度制约模型的稳定性,Neimark-Sacker分支的存在性以及稳定性。利用特征值理论和Jury判据给出模型正平衡态局部渐近稳定的充分条件及分支参数范围,基于规范化理论及中心流形定理,研究了分支的方向及稳定性;通过实例与数值模拟验证所得结论的正确性、可实现性和模型复杂的动力学行为。

The stability and Neimark-Sacker bifurcation of a single population of ratio density-dependent model with time delay, intererence and piecewise constant variables are investigated. The local stability sufficient condition and the range of the parammeter for existence of Neimark-Sacker bifurcation of this model are derived by using the theory of characteristic value. Furthermore, the direction and stability of N-S bifurcation are derived by using the bifurcation theory and the center manifold theorem. Finally, some examples and numerical simulations are presented to illustrate the correctness and realizability of the theoretical results and the complex dynamical behaviors of this model.