摘要
研究一类具有时滞和比率依赖型功能反应函数的食饵-捕食者模型的动力学行为,分析表明系统的渐近稳定关键依赖于时滞。通过选择时滞作为参数,分析了系统从正平衡点处产生极限环的Hopf分支问题,同时得到了系统正平衡点稳定的时滞范围为0<τ<τ+,给出数值模拟验证了作者所得结果的正确性。最后给出本文的主要结论:当τ∈[0,τ0)时,系统(2)的平衡点是渐近稳定的,当τ=τkj,k=1,2,3,4;j=0,1,2,…时,系统(2)在平衡点附近产生Hopf分支,时滞长度为τ。
In this paper,the dynamics of a delayed predator-prey model with ratio-dependent type functional response are considered.We show that the asymptotic behavior depends crucially on the time delay parameter.We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the positive equilibrium.By choosing the the delay as a bifurcation parameter,the length of delay which preserves the stability of the positive equilibrium is calculated（i.e.,0ττ＋）.Some numerical simulation for justifying the analytical findings is also provided.Main conclusions are as follows： the positive equilibrium of the system is asymptotically stable for τ∈[0,τ0）.The system undergoes a Hopf bifurcation at the positive equilibrium when τ=τjk,k=1,2,3,4;j=0,1,2,…,and the length of delay is τ＋.
出处
《重庆师范大学学报（自然科学版）》
CAS
2011年第3期43-48,共6页
Journal of Chongqing Normal University:Natural Science
基金
国家自然科学基金(No.10771215)
湖南省教育厅资助科研项目(No.10C0560)
湖南省科技计划资助项目(No.2010FJ6021)
湖南工程学院科研启动项目(No.0744)
