一类改进的Leslie型捕食与被捕食系统的动力学分析  

Study on Dynamics of a Modified Leslie Predator-Prey System

作　　者：陈玉明[1] 李群宏[1] 徐德贵[1] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《广西科学》2011年第1期7-10,共4页Guangxi Sciences

基　　金：广西壮族自治区自然科学基金项目(2010GXNSFA013110);广西壮族自治区青年科学基金项目(0832014)资助

摘　　要：综合考虑对Leslie型捕食与被捕食系统影响较大的一些因素,提出一类改进的Leslie型捕食与被捕食系统.应用非线性动力学、多项式系数关系等理论及Lyapunov系数方法研究改进系统的动力学行为,得到系统存在稳定平衡点及Hopf分岔等情形时参数应满足的条件,并通过数值仿真验证所得结果是正确的.This paper presented a modified Leslie predator-prey system in which several important factors were considered.The theory of non-linear dynamics,Routh-Hurwitz theorem and the method of Lyapunov coefficient were applied to investigate the dynamical behaviors of the modified system.Then,the necessary parameter conditions for the appearance of the steady equilibrium and the Hopf bifurcation were obtained.Finally,the discussion was verified by numerical simulation.

关 键 词：非线性理论 Leslie系统 HOPF分岔 Bautin分岔 

分 类 号：O175[理学—数学]