一类时滞红松种群模型的动力学行为研究

摘要

In this paper, a kind of Pinus koraiensis ecological system with time delay including pine seeds, squirrels and seedlings is considered. The effect of time delay on stability of the equilibrium and Hopf bifurcation has been studied. And the results show that the delay may cause a stable equilibrium to become unstable, Hopf bifurcation occurs. The direction and stability of the Hopf bifurcation periodic solution bifurcating from Hopf bifurcation at the positive equilibrium is obtained by using the normal form theory and center manifold theory. Numerical simulation with some hypothetical sets of data has been done to support the analytical findings.%研究了一类高维时滞非线性松籽、鼠类和幼苗的红松林生态系统的动力学行为，讨论了时滞对平衡点的稳定性和 Hopf 分支影响，指出了随着时滞的变化，平衡点由稳定变为不稳定，产生Hopf 分支现象，并且考虑周期解的方向和限制在中心流形上该周期解的稳定性。数值模拟例证了分析结果。