一类微分代数捕食-食饵系统的离散化及其定性分析

研究了一类生态经济模型在R3＋内的离散化模型及其动力学行为。首先用庞克莱方法将一类微分代数捕食-食饵系统离散化,得到本文所研究的离散奇异系统。然后通过运用微分代数系统理论与分支理论讨论了模型的平衡点的局部稳定性和分支问题,证明了Neimark-Sacker分支的存在性,并选取捕捞行为的经济利益m作为分支参数,研究了Neimark-Sacker分支及其方向;最后通过数值模拟证明了我们的结果,并展现了模型的复杂的动力学行为。

Discretization and qualitative analysis of a differencial-algebraic predator-prey system

In this paper,we analyze the discretization and the dynamical behaviors of a bioeconomic model in the closed first quadrant R3＋.First,applying the Poincare scheme,we discrete the continuous-time predator-prey system and propose discrete singular system.By using the differential-algebraic system theory and bifurcation theory,local stability and bifurcation of the proposed model around interior equilibrium is discussed,and prove that Neimark-Sacker bifurcation exists.Then we analyze Neimark-Sacker bifurcation and its direction by choosing the economic interest m of harvesting as the parameter of the bifurcation.Finally,numerical simulations are presented not only to illustrate the theoretical results,but also to exhibit complex dynamical behavious of the model.