带有双时滞和环境容纳量的分数阶有毒食饵-捕食者收获模型的Hopf分岔分析  

Hopf Bifurcation Analysis of a Fractional-Order Toxic Predator-Prey Harvesting Model with Double Time Delays and Environmental Carrying Capacity

作　　者：周永雯 余波[1] ZHOU Yongwen;YU Bo(School of Mathematics and Science,Yuxi Normal University,Yuxi 653100,China)

机构地区：[1]玉溪师范学院数理学院,云南玉溪653100

出　　处：《玉溪师范学院学报》2024年第6期1-11,共11页Journal of Yuxi Normal University

基　　金：云南省大学生创新创业训练计划(202211390005).

摘　　要：通过对一类分数阶有毒食饵-捕食者收获模型的动力学分析,建立了含不同时滞和带有环境容纳量的分数阶模型.在明确了分数阶系统存在正平衡点的条件下,分别以两个时滞作为分岔参数,利用分数阶微积分理论、拉普拉斯变换等数学方法进行推导,用以研究系统的稳定性和Hopf分岔,并给出系统产生Hopf分岔的条件,最后借助数学软件进行数值模拟,验证理论分析的正确性.The paper conducts a dynamic analysis of a class of fractional-order toxic predator-prey harvesting model and establishes a fractional-order model with different time delays and environmental carrying capacity.Under the condition that the positive equilibrium point of the fractional-order system exists,with two time delays as bifurcation parameters respectively,the stability and Hopf bifurcation of the system are studied by using the theory of fractional calculus,Laplace transform and other mathematical methods,and the conditions for the occurrence of Hopf bifurcation of the system are given.Finally,numerical simulation is carried out with the help of mathematical software to verify the correctness of the theoretical analysis.

关 键 词：时滞 分数阶 HOPF分岔 有毒食饵-捕食者模型 

分 类 号：O175.12[理学—数学]