Abstract
In this paper, we consider the population growth of a single species living in a two-dimensional spatial domain. New reaction-difusion equation models with delayed nonlocal reaction are developed in two-dimensional bounded domains combining diferent boundary conditions. The important feature of the models is the reflection of the joint efect of the difusion dynamics and the nonlocal maturation delayed efect. We consider and ana- lyze numerical solutions of the mature population dynamics with some wellknown birth functions. In particular, we observe and study the occurrences of asymptotically stable steady state solutions and periodic waves for the two-dimensional problems with nonlocal delayed reaction. We also investigate numerically the efects of various parameters on the period, the peak and the shape of the periodic wave as well as the shape of the asymptotically stable steady state solution.
Highlights
We focus on the numerical computation and analysis of the mature population dynamics on the two-dimensional bounded domains with some well-known birth functions combining with Neumann and Dirichlet boundary conditions
We developed some new Reaction Diffusion Equation (RDE) models with delayed nonlocal reaction for the growth dynamics of a single species population living in a two-dimensional bounded domain
The models reflect the joint effect of the diffusion dynamics and the nonlocal maturation delayed effect
Summary
The problems with delayed nonlocal effects in a one-dimensional bounded domain have recently been studied in [5] by Liang, So, Zhang and Zou. we will focus on the numerical computation and numerical analysis of 2-D reaction-diffusion equation models with delayed nonlocal reaction combining with Neumann and Dirichlet boundary conditions. By using the finite difference method coupled with the iterative technique described, we can obtain the numerical solutions of the two-dimensional reaction-diffusion equation with delayed nonlocal reaction.
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