Dynamics of a Diffusive Model with Spatial Memory and Nonlinear Boundary Condition (Journal of Nonlinear Modeling and Analysis, 2025)
In this paper, we investigate the existence and stability of steady-state and periodic solutions for a heterogeneous diffusive model with spatialmemory 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 bifurcationoccurs regardless of time delay. Conversely, when the interior reaction term isstronger than the boundary reaction term, the presence of Hopf bifurcation isdetermined by the spatial memory delay.
Keywords: Spatial memory; stability; Hopf bifurcation; nonlinear boundary condition.