具有时滞和分段常数变量的食物有限模型的稳定性与分支分析(英文)

Stabilityand bifurcation analysis of the food-limited model with time delay and piecewise constant variables

讨论了具有时滞和分段常数变量的食物有限模型的局部稳定性以及翻转分支和Neimark-Sacker分支.利用分段常数理论、中心流行定理以及分支理论得到翻转分支和Neimark-Sacker分支稳定的充分条件.通过举例和数值模拟验证了所得结论的正确性与可行性,并充分体现了该单种群生物系统复杂的动力学行为.

The stability,flip bifurcation and Neimark-Sacker bifurcation of a discrete-time single population model with food-limited and time delay are investigated in this paper.The sufficient conditions for existence and stability of bifurcation are derived by using piecewise constant arguments,center manifold theorem and bifurcation theory.Numerical simulations are presented not only to illustrate our results with the theoretical analysis,but also to exhibit the complex dynamical behaviors.