时滞分数阶生态流行病系统的稳定性与分支分析  

Stability and bifurcation analysis of delayed fractional order ecological epidemic systems

作　　者：杨国弘 郑巍 YANG Guohong;ZHENG Wei(School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,黑龙江哈尔滨150080

出　　处：《东北师大学报(自然科学版)》2025年第1期39-45,共7页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12271144);黑龙江省属高校基本科研业务费项目(2022-KYYWF-1102);2021年度黑龙江省留学回国人员资助项目。

摘　　要：提出了一个时滞分数阶生态流行病模型,研究了其动力学演化特征并讨论了对该模型的控制策略,研究了不含控制器时系统的稳定性和Hopf分支问题.在考虑控制器的影响下,讨论了系统的稳定性和Hopf分支问题,并指出增加反馈控制的延迟可以改变系统的稳定性.此外,对系统分支问题中控制器中反馈控制时滞产生的影响进行了单独的研究.通过数值模拟对理论结果的正确性进行了验证.A delayed fractional order ecological epidemic model is proposed,the dynamic evolution characteristics of the model are studied,and the control strategy for the model is discussed.The stability and Hopf bifurcation of the system is investigated without a controller.When considering the influence of the controller,the stability of the system and the Hopf branch problem are discussed,and it is pointed out that increasing the delay of feedback control can change the stability of the system.In addition,a separate study on the impact of feedback control delay in the controller for system bifurcation problem is conducted.The correctness of the theoretical results through numerical simulation are verified.

关 键 词：生态流行病模型 分数阶 时滞 HOPF分支 

分 类 号：O29[理学—应用数学]