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A minimalistic model of tree-grass interactions using impulsive differential equations and non-linear feedback functions of grass biomass onto fire-induced tree mortality

机译:利用脉冲微分方程和草类生物量对火灾引起的树木死亡率的非线性反馈函数的树草相互作用的简约模型

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摘要

Since savannas are important ecosystems around the world, their long term dynamics is an important issue, in particular when perturbations, like fires, occur more or less often. In a previous paper, we developed and studied a tree-grass model that take into account fires as pulse events using impulsive differential equations. In this work, we propose to improve this impulsive model by considering the impact of pulse fire on tree biomass by means of combination of two nonlinear functions of grass and tree biomasses respectively. By considering two impact functions, our model yields more complex dynamics, allowing for the possibility of various bistabilities and periodic solutions, in either grassland or savanna states in the ecosystem. Our mathematical analysis allows extensive and realistic description of savannas ecosystems, than previous modelling approaches. We also highlight several threshold parameters that summarize all possible dynamics, as well as three main parameters of bifurcations in the tree-grass dynamics: the fire period, the tree-grass facilitation/competition parameter, and the fire intensity. Using an appropriate nonstandard numerical scheme, we provide numerical simulations to discuss some ecologically interesting cases that our model is able to exhibit along a rainfall gradient, observable in Central Africa.
机译:由于稀树草原是全世界重要的生态系统,因此它们的长期动态是一个重要的问题,尤其是在诸如火之类的扰动或多或少地发生时。在先前的论文中,我们开发并研究了一种树草模型,该模型使用脉冲微分方程将火灾视为脉冲事件。在这项工作中,我们建议通过分别结合草和树木生物量的两个非线性函数,考虑脉冲火对树木生物量的影响,来改进该脉冲模型。通过考虑两个影响函数,我们的模型产生了更复杂的动力学,从而在生态系统中的草原或热带稀树草原州实现了各种双稳性和周期解的可能性。与以前的建模方法相比,我们的数学分析允许对热带稀树草原生态系统进行广泛而现实的描述。我们还将重点介绍几个阈值参数,这些参数概述了所有可能的动态,以及树草动态中的三个主要分叉参数:着火期,树草疏通/竞争参数和着火强度。使用适当的非标准数值格式,我们提供了数值模拟,以讨论我们的模型能够在中非非洲观察到的沿降雨梯度展现的一些生态有趣的案例。

著录项

  • 来源
    《Mathematics and computers in simulation》 |2017年第3期|265-297|共33页
  • 作者单位

    Faculty of Science, University of Yaounde Ⅰ, Cameroon,CETIC, University of Yaounde Ⅰ, Cameroon;

    CIRAD, Umr AMAP, Montpellier, France;

    Faculty of Science, University of Yaounde Ⅰ, Cameroon,LIRIMA, GRIMCAPE, University of Yaounde Ⅰ, Cameroon,CETIC, University of Yaounde Ⅰ, Cameroon;

    University of Douala, Cameroon,LIRIMA, GRIMCAPE, University of Yaounde Ⅰ, Cameroon,CETIC, University of Yaounde Ⅰ, Cameroon;

    IRD, Umr AMAP, Montpellier, France,Plant Systematic and Ecology Laboratory, Department of Biology, Higher Teachers' Training College, University of Yaounde Ⅰ, P.O.Box 047 Yaounde, Cameroon;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Tree-grass interactions; Fires; Impulsive differential equations; Asymptotic stability; Bifurcation;

    机译:草与草的相互作用;火灾;脉冲微分方程渐近稳定性;分叉;

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