Periodic Dynamics of a Reaction-Diffusion-Advection Model with Michaelis–Menten Type Harvesting in Heterogeneous Environments

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-09-12 DOI:10.1137/23m1600852

Yunfeng Liu, Jianshe Yu, Yuming Chen, Zhiming Guo

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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 5, Page 1891-1909, October 2024.
Abstract. Organisms inhabit streams, rivers, and estuaries where they are constantly subject to drift and overfishing. Consequently, these organisms often confront the risk of extinction. Can a reasonable fishing ban satisfy the human need for sufficient aquatic proteins without depleting fishery resources? We propose a reaction-diffusion-advection model to answer this question. The model consists of two subequations, which are constantly switched to describe closed seasons and open seasons with Michaelis–Menten type harvesting. We define a threshold value [math] for the duration of the fishing ban ([math]) and establish the relationships between [math] and each of the downstream end [math], the advection rate [math], and the diffusion rate [math]. Under certain conditions, the trivial equilibrium point 0 is globally asymptotically stable if [math]. When [math], we obtain sufficient conditions on the existence of a globally asymptotically stable periodic solution based on the thresholds in all parameter settings. Finally, some discussions on our findings are provided.

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异质环境中具有 Michaelis-Menten 型收获的反应-扩散-平流模型的周期动力学

SIAM 应用数学学报》第 84 卷第 5 期第 1891-1909 页，2024 年 10 月。摘要生物栖息在溪流、河流和河口，经常受到漂流和过度捕捞的影响。因此，这些生物经常面临灭绝的危险。合理的禁渔能否在不耗尽渔业资源的情况下满足人类对充足水生蛋白质的需求？我们提出了一个反应-扩散-对流模型来回答这个问题。该模型由两个子方程组成，这两个子方程不断切换，以描述迈克尔-门顿式捕捞的休渔期和开渔期。我们定义了禁渔期（[math]）的临界值[math]，并建立了[math]与下游末端[math]、平流速率[math]和扩散速率[math]之间的关系。在一定条件下，如果[math]，则微分平衡点 0 是全局渐近稳定的。math]时，我们根据所有参数设置下的阈值，得到了全局渐近稳定周期解存在的充分条件。最后，对我们的发现进行了一些讨论。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.