食饵具有Allee效应的离散捕食-被捕食系统的分岔及控制  

Bifurcations and Controls of a Discrete-time Predator-prey System with Allee Effect on Prey

作　　者：王涛 古佳忻 张莉敏 WANG Tao;GU Jia-xin;ZHANG Li-min(School of Science,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]重庆邮电大学理学院,重庆400065

出　　处：《科学技术与工程》2025年第7期2664-2672,共9页Science Technology and Engineering

基　　金：国家自然科学基金(11901073);教育部产学合作协同育人项目(230904084192851);重庆市高等教育学会2023—2024年度高等教育科学研究课题(cqgj23047C)。

摘　　要：为探讨Allee效应对种群动态行为的影响,利用中心流形定理与分岔理论,研究了一类食饵具有Allee效应的离散捕食-捕食者系统的分岔。结果表明:适当增大食饵种群的增长率,会导致系统通过跨临界分岔出现食饵的天敌——捕食者;在适当的Allee效应下,系统是稳定的,但Allee效应超过临界值,系统会发生二倍周期的翻转分岔,分岔参数图还表明随着Allee效应进一步增强,此二倍周期的翻转分岔会导致系统出现混沌。从生物学的观点来看,在一定的生态环境中,某一物种繁殖到一定程度,会通过“物竞天择”的方式出现其天敌;适当的Allee效应有利于捕食系统的稳定,但食饵Allee效应过强,将造成捕食效能锐减,失去天敌的有效制约,食饵将经历短暂地激增、然后超过环境容纳量而消亡。为减少分岔带给系统的不利影响,利用状态反馈法控制跨临界分岔、利用混合策略控制翻转分岔。数值模拟结果显示与理论分析完全一致。To investigate the influence of Allee effect on population dynamics,the center theorem and bifurcation theory were used to study the bifurcation of a discrete predator-prey system with Allee effect on prey.The results indicate that an appropriate increase in the growth rate of the prey population will lead to the emergence of predators,the natural enemies of the prey by the transcritical bifurcation;Under the appropriate Allee effect,the system is stable,but if the Allee effect exceeds the critical value the system will undergo a double period flip bifurcation.The bifurcation parameter diagram also shows that as the Allee effect further strengthens,this flip bifurcation will lead to chaos in the system.From a biological perspective,in a certain ecological environment,a species that reproduces to a certain extent will encounter its natural enemies through“natural selection”.An appropriate Allee effect is beneficial for the stability of the predator-prey system,but if the Allee effect of the prey is too strong,it will cause a sharp decrease in predators and an effective restriction of no natural enemies.The prey will undergo a brief surge,exceed the environmental capacity,and then die out.To reduce the adverse effects of the bifurcations on the system,the state feedback is used to control the transcritical bifurcation and facilitate hybrid control to control the flip bifurcation.The numerical simulation results show complete consistency with the theoretical analyses.

关 键 词：跨临界分岔 翻转分岔 分岔控制 数值模拟 

分 类 号：O29[理学—应用数学]