基于FEPG的一类岛屿种群繁衍扩散模型的有限元求解

A Finite Element Solution for a Class of Island Population Diffusion Model Based on FEPG

本文对岛屿环境下一类种群繁衍扩散模型进行了研究,给出了方程的弱解形式,利用有限元程序自动生成系统(FEPG)对种群密度的时空分布变化进行了数值模拟.数值模拟结果表明:当空间扩散系数相对较大时,种群密度空间分布具有周期性,形成一个密度波由中心区域向外传播;当扩散系数很小时,种群密度空间分布不具有空间周期性现象,逐步趋向一个稳定均匀分布状态.

In this paper,a class of island population diffusion model has been studied and given the weak solution of the equation.Using the finite element automatic generating system(FEPG),we simulate the spatial distribution change of population density.The simulation results show that:when the spatial diffusion coefficient is relatively large,spatial distribution of population density has spatial periodicity and forms a density wave spreading outward from the central region;when the diffusion coefficient is very small,the spatial distribution of population density does not have a cyclical phenomenon,and gradually tends to a steady uniform distribution.