研究了一类一阶非线性时滞微分方程描述的TCP系统的动力学行为.通过分析其相应的特征超越方程,得到了当时滞通过一系列临界值时,在正平衡点处Hopf分支产生.利用中心流形和规范型理论,得到了确定Hopf分支方向和稳定性的具体计算表达式.运用Wu[Trans Amer Math Soc, 1998,350(12): 4799-4838]的方法,得到了全局Hopf分支存在的条件
摘要(英文)：
The dynamics of a TCP system described by a first-order nonlinear delay differential equations was investigated. By analyzing the associated characteristic transcendental equation, the result that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay passes through a sequence of critical values was obtained. Explicit algorithms for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were derived by using the normal form theory and center manifold theory. Global exist...
