时滞分数阶生态流行病系统的动态演化分析  

Dynamic Evolution Analysis of Time-delay Fractional-order Ecological Epidemic Systems

作　　者：王飞龙 肖敏 赵静 WANG Feilong;XIAO Min;ZHAO Jing(College of Automation and College of Artificial Intelligence,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)

机构地区：[1]南京邮电大学自动化学院、人工智能学院,江苏南京210023

出　　处：《控制工程》2024年第8期1496-1503,共8页Control Engineering of China

基　　金：国家自然科学基金资助项目(62073172,61573194);江苏省自然科学基金资助项目(BK20181389);江苏省研究生科研与实践创新计划项目(KYCX21_0754)。

摘　　要：为研究时滞分数阶系统的动力学演化特征,提出一个时滞分数阶生态流行病模型。首先,分析了平衡点稳定性和Hopf分岔特性,发现当时滞参数小于分岔点时,系统的正平衡点处是渐近稳定的;当时滞参数大于分岔点时,系统在正平衡点处发生Hopf分岔。其次,讨论了控制项的反馈增益对平衡点稳定性和分岔动力学的影响机制,阐明了分岔点随着反馈增益的增大而减小,即可以通过减小反馈增益来改良系统的稳定性。最后,通过数值仿真对理论结果的正确性进行了验证。In order to explore the dynamic evolution characteristics of time-delay fractional order systems,a fractional order ecological epidemic model with time-delay is proposed.Firstly,we analyze the stability of the equilibriua and Hopf bifurcation characteristics of the fractional-order ecological epidemic system with time delay.It is found that the system is asymptotically stable at the positive equilibrium point when the time delay is less than the bifurcation point;When the time-delay is greater than the bifurcation point,the Hopf bifurcation occurs at the positive equilibrium point.Secondly,we discuss the influence of the feedback gain in the control term on the stability and Hopf bifurcation.It is revealed that the bifurcation point decreases with the increase of the feedback gain,that is,the stability of the system can be improved by reducing the feedback gain.Finally,the correctness of the theoretical results is verified by numerical simulations.

关 键 词：生态流行病学模型 动态演化分析 分数阶 时滞延迟 HOPF分岔 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]