带有修正Leslie-Gower项的密度抑制种群数学模型斑图研究

Study on the pattern of mathematical model of density inhibition population with modified Leslie-Gower term

摘要

针对一类带有修正Leslie-Gower项的密度抑制种群数学模型斑图的存在性,利用偏微分方程线性稳定性理论,在不含扩散项和含有扩散项时,对常数定态解稳定性分别进行研究,得到了模型斑图存在的条件.通过数值仿真验证了理论的正确性,结合理论分析和数值仿真,给出了模型在生态系统中的现实意义.

Abstract

In response to the existence of a density inhibition population mathematical model with modified Leslie-Gower terms, the stability of constant steady-state solutions was studied by using the linear stability theory of partial differential equations, both with and without diffusion terms, and the conditions for the existence of model patterns were obtained. The correctness of the theory was verified by numerical simulation, and the practical significance of the model in the ecosystem was presented by combining theoretical analysis and numerical simulation.

关键词

斑图 / 密度抑制 / 稳定性

Key words

pattern / density inhibition / stability

参考文献

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