Theoretical mechanism of boundary-driven instability of the reaction–diffusion population system

Author:

Song Yong-Li12ORCID,Yang Gao-Xiang13ORCID

Affiliation:

1. School of Mathematics and Statistics, Ankang University, Ankang, Shaanxi 725000, P. R. China

2. School of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China

3. Institute of Mathematics and Applied Mathematics, Ankang University, Ankang, Shaanxi 725000, P. R. China

Abstract

In this paper, we study the stability of a constant equilibrium solution of the reaction–diffusion population equation under different boundary conditions through analysis of its characteristic equation. In a scalar reaction–diffusion equation, we have found that the stability of a constant equilibrium solution is different when the scalar reaction–diffusion equation is subject to Neumann boundary conditions, Dirichlet boundary conditions and the mixed type boundary conditions, respectively. Similarly, the more complex results are found in the two reaction–diffusion equations with all different kinds boundary conditions. The relevant numerical calculation results are carried out to demonstrate the validity of theoretical analysis.

Funder

National Natural Science Foundations of China

Zhejiang Provincial Natural Science Foundation of China

Natural Science Basic Research Program of Shaanxi

Research Fund of Ankang University

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation

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