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首页> 外文期刊>Journal of Theoretical Biology >Mathematical model for the dynamics of Savanna ecosystem considering fire disturbances
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Mathematical model for the dynamics of Savanna ecosystem considering fire disturbances

机译：考虑火灾干扰的大草原生态系统动态的数学模型

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In this article, the stability of equilibrium solutions of a recently formulated mathematical model of Savanna ecosystem is analytically and numerically analyzed. The mathematical model is formulated by generalizing all plant life into three components; trees, tree saplings, and grass under ecologically valid effects of fire, rainfall and competition for space. Fire has a considerable effect on trees by delaying the recruitment of saplings to trees and the recruitment rate is a piecewise linear decreasing function of grass with a sigmoidal shape. This leads to there existing different equilibria in the plant community of a Savanna ecosystem. It is rigorously demonstrated that the local stability of equilibria depends on the slope and value of the recruitment function. Moreover, it is found that the composition of high grass cover and low tree cover or low grass cover and high tree cover are the stable equilibria, while intermediate cover results in unstable equilibria. In analyzing the global stability of solutions, it is found that the limit set is an equilibrium solution. Several numerical simulations are provided to validate the analytical studies of the behavior of the equilibrium solutions. The numerical solutions are generated using a Python ordinary differential equation(ODE) solver. The analytical and numerical solutions presented in this work are very important for further developments in the area of mathematical ecology. (C) 2020 Elsevier Ltd. All rights reserved.
机译：本文对最近建立的热带草原生态系统数学模型的平衡解的稳定性进行了分析和数值分析。数学模型是通过将所有植物的生命归纳为三个组成部分而建立的；树木、树苗和草在火灾、降雨和空间竞争的生态有效影响下。火灾通过延迟树苗向树木的补充而对树木产生相当大的影响，补充率是具有S形形状的草的分段线性递减函数。这导致热带草原生态系统的植物群落存在不同的平衡。严格证明了平衡点的局部稳定性取决于补充函数的斜率和值。此外，还发现高草覆盖和低树覆盖或低草覆盖和高树覆盖的组成是稳定平衡，而中间覆盖导致不稳定平衡。在分析解的全局稳定性时，发现极限集是一个平衡解。通过数值模拟验证了平衡解行为的分析研究。数值解是使用Python常微分方程（ODE）求解器生成的。本文给出的解析解和数值解对于数学生态学领域的进一步发展非常重要。（C） 2020爱思唯尔有限公司版权所有。

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