摘要
研究一类具有时滞的Gompertz增长率的捕食-被捕食模型,通过分析特征方程讨论了正平衡点的局部稳定性;通过构造适当的Lyapunov泛函,得到了保证系统正平衡点全局渐近稳定的充分条件,并讨论了在正平衡点附近Hopf分支的存在性问题.当τ=0时,应用微分方程定性理论,得到了系统存在极限环的充分条件.
A predator-prey model with time delay and Gompertz growth rate is investigated.The local stability of a positive equilibrium is discussed by analyzing the corresponding characteristic equation.By constructing a suitable Lyapunov functional,the sufficient conditions are derived for the global asymptotic stability of the positive equilibrium.The existence of Hopf bifurcation is also addressed.When the time delay equals to 0,by using the qualitative theory of ordinary differential equations,the sufficient condition is obtained for the existence of limit cycle.
出处
《北华大学学报（自然科学版）》
CAS
2011年第1期18-22,共5页
Journal of Beihua University（Natural Science）
基金
国家自然科学基金项目(10671209,11071254)
