Thursday, September 29, 2022

Time: 16:10-17:00

VENUE： Mathematics Building Room 312

Speaker: Prof. Jia-Yuan Dai

Department of Applied Mathematics, National Chung Hsing University

Title:

Dynamics of two predators competing for a renewable prey

Abstract

We are interested in finding stable ‘large’ periodic orbits of an ODE system that describes the dynamics of two predators competing for the same prey. The prey population grows logistically in the absence of predation, and the predators feed on the prey with Holling’s type-II response. We first briefly explain a characterization of parameter regions that may support coexistence states. Then we explain how stable ‘large’ periodic orbits are triggered by perturbing an elliptic Hopf bifurcation point without parameters. For this aim, we prove that the ODE system admits an elliptic Hopf bifurcation and discuss an attempt by using the averaging method. This is an ongoing research with A. López Nieto, P. Lappicy, H. Stuke, and N. Vassena.