余维数
捕食者
常量(计算机编程)
捕食
数学
产量(工程)
分叉
数学分析
物理
生物
计算机科学
生态学
非线性系统
热力学
量子力学
程序设计语言
出处
期刊:Discrete and Continuous Dynamical Systems-series B
[American Institute of Mathematical Sciences]
日期:2024-01-01
标识
DOI:10.3934/dcdsb.2024061
摘要
The bifurcation analysis of a predator-prey system with Holling-II functional response function and constant-yield predator releasing rate is carried out in this paper, which is a fundamental model for studying pulse control strategies or switching strategies based on the threshold level of the pest population. We show that the system can have at most two positive equilibria, and can undergo a sequence of bifurcations, including transcritical bifurcation, pitchfork bifurcation, saddle-node bifurcation, Hopf bifurcation, degenerate Hopf bifurcation of codimension 2, and Bogdanov-Takens bifurcation of codimensions 2 and 3. Complex dynamics, such as multi-steady states, the existence of a semi-stable limit cycle, a homoclinic loop, and multiple coexistent periodic orbits, are revealed. These results show that the constant-yield predator releasing rate can be used to organize the complex dynamics and bifurcations of the model. The proposed model with constant-yield predator releasing rate is not only necessary for characterizing many practical problems including integrated pest management, but also can generate more rich bifurcation phenomena and dynamic behaviors.
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