Existence of a Limit Cycle in an Intraguild Food Web Model with Holling Type II and Logistic Growth for the Common Prey

• 作者: Francisco Eduardo Castillo-Santos Iván Loreto-Hernández Miguel Angel Dela Rosa
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Hopf’s BIFURCATION LIMIT Cycle Intraguild Model
• 年，卷（期）: 2017,（3）
• 页码范围: 358-376
• 页数: 19页
• 分类号: O1

摘要

In this paper, we prove the existence of a limit cycle for a given system of differential equations corresponding to an asymmetrical intraguild food web model with functional responses Holling type II for the middle and top predators and logistic grow for the (common) prey. The existence of such limit cycle is guaranteed, via the first Lyapunov coefficient and the Andronov-Hopf bifurcation theorem, under certain conditions for the parameters involved in the system.