结合帮助和妊娠延迟分析猎物-捕食者计划

IF 1.3 4区 数学 Q1 MATHEMATICS Journal of Mathematics Pub Date : 2024-04-10 DOI:10.1155/2024/2708546
M. Mukherjee, D. Pal, S. K. Mahato, Ebenezer Bonyah, Ali Akbar Shaikh
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引用次数: 0

摘要

本文提出了一个由三个物种组成的三维连续时间动力系统,其中两个是相互竞争的猎物,一个是捕食者。我们还假设,在捕食过程中,两队猎物的成员互相帮助,两队猎物的捕食率不同。假设猎物和捕食者之间的相互作用受霍林二型功能反应和捕食者消耗猎物的离散型妊娠延迟的支配。在这项工作中,我们建立了各种平衡点的局部渐近稳定性,以理解模型系统的动力学。我们讨论了平衡解共存的不同条件。通过构建合适的 Lyapunov 函数,讨论了当妊娠延迟为零时,系统的持久性、永恒性以及正内部平衡解的全局稳定性,并且在内部平衡点周围的第一象限状态空间内部不存在周期性轨道。由于我们引入了捕食者妊娠导致的时间延迟,我们还讨论了延迟模型的稳定性。据观察,当妊娠延迟增加到某个临界阈值时,内部平衡点周围会出现稳定性切换。这里出现了霍普夫分岔现象,同时还观察到了与系统周期解相对应的稳定极限循环。这项研究揭示了将延迟作为分岔参数,对所提模型的稳定性也起着重要作用。为了解释我们提出的模型,我们给出了计算机模拟的数值示例。我们还通过适当的数值示例,批判性地探讨了我们的分析结果对生物学的影响。
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Analysis of Prey-Predator Scheme in Conjunction with Help and Gestation Delay
This paper presents a three-dimensional continuous time dynamical system of three species, two of which are competing preys and one is a predator. We also assume that during predation, the members of both teams of preys help each other and the rate of predation of both teams is different. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey. In this work, we establish the local asymptotic stability of various equilibrium points to understand the dynamics of the model system. Different conditions for the coexistence of equilibrium solutions are discussed. Persistence, permanence of the system, and global stability of the positive interior equilibrium solution are discussed by constructing suitable Lyapunov functions when the gestation delay is zero, and there is no periodic orbit within the interior of the first quadrant of state space around the interior equilibrium. As we introduced time delay due to the gestation of the predator, we also discuss the stability of the delayed model. It is observed that the existence of stability switching occurs around the interior equilibrium point as the gestation delay increases through a certain critical threshold. Here, a phenomenon of Hopf bifurcation occurs, and a stable limit cycle corresponding to the periodic solution of the system is also observed. This study reveals that the delay is taken as a bifurcation parameter and also plays a significant role for the stability of the proposed model. Computer simulations of numerical examples are given to explain our proposed model. We have also addressed critically the biological implications of our analytical findings with proper numerical examples.
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来源期刊
Journal of Mathematics
Journal of Mathematics Mathematics-General Mathematics
CiteScore
2.50
自引率
14.30%
发文量
0
期刊介绍: Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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