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Dynamics of a Diffusive Model with Spatial Memory and Nonlinear Boundary Condition
  
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KeyWord:Spatial memory, stability, Hopf bifurcation, nonlinear boundary condition
Author NameAffiliation
Xiangsheng Deng School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China 
Shangjiang Guo School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China 
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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.