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

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.