具有时滞和分段常数变量的比率型密度制约模型的分支分析

The bifurcations of ratio-dependent density restriction model with piecewise constant arguments and time delay

讨论了具有分段常数变量和时滞的比率型密度制约单种群模型的稳定性及分支等问题,运用特征值理论和Jury判据给出模型正平衡态局部渐近稳定的充分条件;利用分支理论及中心流形定理,得到了Flip分支及N-S分支存在的条件,并讨论了N-S分支方向和稳定性;通过实例和数值模拟验证了定理条件与结论的可实现性.

The stability and bifurcations of a single population of ratio-dependent density restriction model with piecewise constant arguments and time delay are investigated.The local stability sufficient conditions of the positive equilibrium are derived by using the theory of characteristic value and Jury criterion.Furthermore the range of the parameter for existence of Neimark-Sacker bifurcation and Flip bifurcation of this model and the direction,stability of N-S bifurcation are achieved 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 our theoretical results.