结点含时滞的具有零和非零时滞耦合的复杂网络混沌同步

Chaotic synchronization in complex networks with delay nodes by non-delay and delay couplings

时滞耦合的复杂网络同步已经有大量的研究成果,而网络结点含时滞的无时滞耦合的复杂网络同步的研究工作较少.为使网络模型更接近现实和适用更广的范围,建立了网络结点含时滞,而耦合兼零时滞(无时滞)和非零时滞(有时滞)的复杂网络同步模型.在网络结点上分别设置线性控制器和自适应控制器,研究了其混沌同步问题.利用李雅普诺夫稳定性定理,设计相应的正定函数,分别给出了复杂网络同步的充分条件.最后,为证实同步方案的有效性,选择时滞Logistic函数为结点动力系统,在兼无时滞和有时滞的网络上,给出了线性反馈控制同步误差数值演化趋势.

The synchronization in complex network model with time-delay nodes is investigated. The model is applicable for two sorts of complex networks. With linear feedback controller and adaptive feedback controller, positive definite functions are designed respec- tively. The sufficient conditions of synchronization are given by Lyapunov stability theory. Finally, numerical simulations show the effectiveness of the synchronization in complex networks.