TY - JOUR
T1 - Dynamics of a Diffusive Model with Spatial Memory and Nonlinear Boundary Condition
AU - Deng , Xiangsheng
AU - Guo , Shangjiang
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 680
EP - 703
PY - 2025
DA - 2025/04
SN - 7
DO - http://doi.org/10.12150/jnma.2025.680
UR - https://global-sci.org/intro/article_detail/jnma/24022.html
KW - Spatial memory, stability, Hopf bifurcation, nonlinear boundary
condition.
AB - <p style="text-align: justify;">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.</p>