Stability and Dynamical Analysis of a Biological System

Author:

Pan Xinhong12,Zhao Min23,Wang Yapei12,Yu Hengguo12,Ma Zengling23,Wang Qi23

Affiliation:

1. School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China

2. Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, China

3. School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325035, China

Abstract

This study considers the spatiotemporal dynamics of a reaction-diffusion phytoplankton-zooplankton system with a double Allee effect on prey under a homogeneous boundary condition. The qualitative properties are analyzed, including the local stability of all equilibria and the global asymptotic property of the unique positive equilibrium. We also discuss the Hopf bifurcation and the steady state bifurcation of the system. These results are expected to help understand the complexity of the Allee effect and the interaction between phytoplankton and zooplankton.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

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