Dynamics of a Diffusive Model with Spatial Memory and Nonlinear Boundary Condition

Abstract

In this paper, we investigate the existence and stability of steady-state and periodic solutions for a heterogeneous diffusive model with spatial memory and nonlinear boundary conditions, employing Lyapunov-Schmidt reduction and eigenvalue theory. Our findings reveal that when the interior reaction term is weaker than the boundary reaction term, no Hopf bifurcation occurs regardless of time delay. Conversely, when the interior reaction term is stronger than the boundary reaction term, the presence of Hopf bifurcation is determined by the spatial memory delay.