Chaos Induced by Snap-Back Repeller in a Two Species Competitive Model

• 作者: Bacim Alali
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Complex Dynamics Snap-Back Repeller Marotto Theorem Persistence Theory BIFURCATION
• 年，卷（期）: 2020,（2）
• 页码范围: 311-328
• 页数: 18页
• 分类号: O17

摘要

In this paper, we investigate the complex dynamics of two-species Ricker-type discrete-time competitive model. We perform a local stability analysis for the fixed points and we will discuss about its persistence for boundary fixed points. This system inherits the dynamics of one-dimensional Ricker model such as cascade of period-doubling bifurcation, periodic windows and chaos. We explore the existence of chaos for the equilibrium points for a specific case of this system using Marotto theorem and proving the existence of snap-back repeller. We use several dynamical systems tools to demonstrate the qualitative behaviors of the system.