Joint Impact of Maturation Delay and Fear Effect on the Population Dynamics of a Predator-Prey System

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-07-22 DOI:10.1137/23m1596569

Xiaoke Ma, Ying Su, Xingfu Zou

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1557-1579, August 2024.
Abstract. In this paper, taking into account the maturation period of prey, we propose a predator-prey model with time delay and fear effect. We confirm the well-posedness of the model system, explore the stability of the equilibria and uniform persistence of the model, and investigate Hopf bifurcations. Moreover, we also numerically explore the global continuation of the Hopf bifurcation. Interestingly, our results show that as the delay increases, the stable and unstable periodic solutions may both disappear and the unstable positive equilibrium may regain its stability. These results reveal how the maturation delay and the fear effect jointly impact the population dynamics of the predator-prey system.

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成熟延迟和恐惧效应对捕食者-猎物系统种群动态的共同影响

SIAM 应用数学杂志》第 84 卷第 4 期第 1557-1579 页，2024 年 8 月。摘要本文考虑到猎物的成熟期，提出了一个具有时间延迟和恐惧效应的捕食者-猎物模型。我们证实了模型系统的拟合性，探讨了模型均衡的稳定性和均匀持久性，并研究了霍普夫分岔。此外，我们还用数值方法探讨了霍普夫分岔的全局持续性。有趣的是，我们的结果表明，随着延迟的增加，稳定和不稳定的周期解可能同时消失，而不稳定的正平衡可能恢复稳定。这些结果揭示了成熟延迟和恐惧效应如何共同影响捕食者-猎物系统的种群动态。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.