【摘要】 证明了随着时滞的增大系统在正平衡点处存在Hopf分支,并用庞加莱规范型方法和中心流行定理详细的讨论了Hopf分支的方向及其产生的周期解得稳定性.不仅从理论上分析了系统的动力学性质,而且还作了相应的数值模拟来检验结果.更多还原

【Abstract】 In this paper,we prove that the sequence of Hopf bifurcations occurs at the positive equilibrium as the delay increases. Explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived,using the theory of normal form and center manifold. The dynamical behaviours are studied both analytically and numerically by computer simnlation.更多还原