流动生境中的反应-扩散-平流变化学模型:数学分析与数值模拟

Wang Zhang, Hua Nie, Jianhua Wu
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引用次数: 1

摘要

本文研究了两种生物生长并竞争单一有限资源的反应-扩散-平流趋化模型。以两种植物的生长速率为可变参数,研究了生长速率对系统动力学的影响。研究发现,存在几个临界曲线,可以将该系统的动力学分为三种情景:(1)两个物种都灭绝;(二)竞争性排斥;(3)共存。此外,我们采用数值方法进一步了解上述临界曲线的潜在行为,并观察到除了竞争排斥和共存之外,还可能出现双稳态现象。为了进一步研究平流和扩散对系统动力学的影响,我们分别给出了随平流速率和扩散速率增加的单种模型和两种模型的正平衡解的分岔图。这些数值结果表明,平流和扩散在决定流动反应器中两种物质竞争的动力学中起着关键作用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Reaction-Diffusion-Advection Chemostat Model in a Flowing Habitat: Mathematical Analysis and Numerical Simulations
This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor.
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