具有年龄结构和比例依赖响应函数的捕食者-食饵模型Hopf分岔

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Discrete and Continuous Dynamical Systems-Series B Pub Date : 2022-01-01 DOI:10.3934/dcdsb.2022082

Tongtong Chen, Jixun Chu

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引用次数: 1

摘要

本文研究了一个具有年龄结构和比例依赖响应函数的捕食者-食饵模型。该模型被表述为一个抽象的非密集定义柯西问题，并给出了正年龄相关平衡存在的充分条件。然后利用非密集区域半线性方程的积分半群理论和Hopf分岔理论，证明了Hopf分岔发生在正年龄相关平衡点上。数值模拟验证了理论结果，并进行了灵敏度分析。结果表明，猎物避难所具有稳定效应，即猎物避难所是维持猎物和捕食者种群平衡的重要因素。

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Hopf bifurcation for a predator-prey model with age structure and ratio-dependent response function incorporating a prey refuge

In this paper, a predator-prey model with age structure and ratio-dependent response function incorporating a prey refuge is investigated. The model is formulated as an abstract non-densely defined Cauchy problem and a sufficient condition for the existence of the positive age-related equilibrium is given. Then using the integral semigroup theory and the Hopf bifurcation theory for semilinear equations with non-dense domain, it is shown that Hopf bifurcation occurs at the positive age-related equilibrium. Numerical simulations are performed to validate theoretical results and sensitivity analyses are presented. The results show that the prey refuge has a stabilizing effect, that is, the prey refuge is an important factor to maintain the balance between prey and predator population.

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来源期刊

Discrete and Continuous Dynamical Systems-Series B 数学-应用数学

CiteScore

2.80

自引率

8.30%

发文量

216

审稿时长

6 months

期刊介绍： Centered around dynamics, DCDS-B is an interdisciplinary journal focusing on the interactions between mathematical modeling, analysis and scientific computations. The mission of the Journal is to bridge mathematics and sciences by publishing research papers that augment the fundamental ways we interpret, model and predict scientific phenomena. The Journal covers a broad range of areas including chemical, engineering, physical and life sciences. A more detailed indication is given by the subject interests of the members of the Editorial Board.