Affiliation:
1. School of Mathematics and Statistics Science Ludong University Yantai China
2. College of Mathematics and Systems Science Shandong University of Science and Technology Qingdao China
Abstract
This paper presents a detailed study on the dynamics of a three‐species food chain system with memory‐based delay under weak Allee effect and middle predator refuge. The local stability analyses of the non‐diffusive and memory‐based diffusion systems are investigated. Moreover, we give a priori estimates and obtain the existence of the positive constant steady state by applying the comparison theorem. Sufficient conditions for the global stability are established by Barbǎlat lemma and the Lyapunov function. The theoretical results suggest the joint effect of cross‐diffusion and memory‐based delay can lead to Hopf bifurcation, which cannot appear in the system with self‐diffusion or a small cross‐diffusion coefficient. Numerical results verify the validity of the theoretical analysis.
Subject
General Engineering,General Mathematics
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