一类带大参数的二维生物模型的快慢动力学与松弛振动

Slow-Fast Dynamics and Relaxation Oscillations in a Two-Dimensional Biological Model with Large Parameters

本文研究一类带大参数、密度依赖的捕食-食饵系统的快慢动力学与松弛振动的存在性.通过对退化系统与层系统流的分析,我们定义了奇异鞍点、奇异结点并考虑其摄动,得到了系统平衡点稳定性及其类型;接着,根据正平衡点的不同位置并基于匹配渐近展开和几何奇摄动理论,我们研究了系统经典松弛振动的存在性问题;数值模拟验证了结论的正确性.

This paper studies the fast-slow dynamics and the existence of relaxation oscillations in a predator-prey system with large parameter and density-dependent. Based on the analysis on the fast-slow flows of the reduced and layer systems, we define the singular saddles and the singular nodes and then consider their singular perturbation, the stability and the types of the equilibriums of the system are analyzed. According to the different positions of the positive equilibrium, we show the existence of classical relaxation oscillations in the system by the method of matching asymptotic expansion and geometric singular perturbation theory. The theoretical results are verified by numerical simulations finally.