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

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.