摘要
研究了参数依赖时滞的Nicholson生态模型的稳定性和分支问题.利用几何分析方法和摄动法,给出了系统唯一正平衡态的稳定性和Hopf分支存在条件,得到了分支周期解的近似解析表达式和周期解稳定性判别式,通过若干实例验证了理论分析和数值计算的一致性.
The dynamics of a delayed Nicholson blowflies equation with delay-dependent parameters are investigated.We prove geometrically that a finite number of Hopf bifurcations occur between two critical values of time delayτ.By using the perturbation approach, an approximation to the bifurcating periodic solution and the formulas for determining the direction and stability of the Hopf bifurcations are derived.Finally,some numerical examples supporting our theoretical predictions are also given.
出处
《应用数学学报》
CSCD
北大核心
2010年第5期824-839,共16页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(60134010
60671063)资助项目
关键词
时滞微分方程
稳定性
HOPF分支
摄动法
delay differential equations
stability
Hopf bifurcation
perturbation approach
