不连续耦合的时滞复杂动态网络的同步

基于李雅普诺夫稳定性理论,对不连续耦合的时滞复杂动态网络进行分析,得到网络同步的充分条件,并且给出网络实现同步时滞的上界估计。研究表明:即使网络之间的耦合是不连续的,只要时滞满足一定条件,网络也可以实现同步,且网络容许的时滞上界与耦合强度、网络代数连通性以及耦合的开关率相关。数值模拟中利用Ikeda系统作为节点动力学,采用误差函数作为网络同步性指标,给出网络同步误差演化轨迹和各状态的演化轨迹,并进一步分析控制参数对同步速度的影响,模拟结果验证了理论结果的正确性。

Synchronization of time-delayed complex dynamical networks with discontinuous coupling

The synchronization problem of complex dynamical networks with time delay and discontinuous coupling was investigated based on Lyapunov stability theory. The sufficient conditions for the networks synchronization was established and the upper bound estimation of the time delay was obtained. The acquired analytical results showed that network with discontinuous coupling could achieve synchronization if time delay met some conditions. The upper bound of the delay for synchronization depended on the coupling strength, the algebraic connectivity of network and on-off rate. The application of numerical simulation results proved that evolution trajectory of network synchronization error and different conditions, in which Ikeda system was used as node dynamics and error function as the network synchronization index. Furthermore, the effect of control parameters on the synchronization speed was analyzed. Numerical examples were provided to verify the effectiveness of the theoretical results.