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Mathematical model for the dynamics of Savanna ecosystem considering fire disturbances
Journal of Theoretical Biology ( IF 2 ) Pub Date : 2020-10-11 , DOI: 10.1016/j.jtbi.2020.110515
Kewani Welay Brhane 1 , Michael Gidey Gebru 2 , Abdulaziz Garba Ahmad 3
Affiliation  

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.



中文翻译:

考虑火灾干扰的热带稀树草原生态系统动力学数学模型

在本文中,对最近建立的热带稀树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。通过将所有植物的生命概括为三个部分来制定数学模型。树木,树苗和草在火灾,降雨和空间竞争的生态有效影响下发挥作用。火通过延迟幼树向树的募集而对树具有相当大的影响,并且募集速率是具有S形形状的草的分段线性递减函数。这导致在稀树草原生态系统的植物群落中存在不同的平衡。严格证明均衡的局部稳定性取决于募集函数的斜率和值。此外,结果表明,高草皮与低树皮或低草皮与高树皮的组成是稳定的平衡,而中间草皮则导致不稳定的平衡。在分析解的整体稳定性时,发现极限集是一个平衡解。提供了一些数值模拟,以验证对平衡溶液行为的分析研究。数值解是使用Python常微分方程(ODE)求解器生成的。这项工作中提出的解析和数值解决方案对于数学生态学领域的进一步发展非常重要。发现极限集是一个平衡解。提供了一些数值模拟,以验证对平衡溶液行为的分析研究。数值解是使用Python常微分方程(ODE)求解器生成的。这项工作中提出的解析和数值解决方案对于数学生态学领域的进一步发展非常重要。发现极限集是一个平衡解。提供了一些数值模拟,以验证对平衡溶液行为的分析研究。数值解是使用Python常微分方程(ODE)求解器生成的。这项工作中提出的解析和数值解决方案对于数学生态学领域的进一步发展非常重要。

更新日期:2020-10-17
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