中文摘要：

基于随机牵制控制对同时存在无时滞耦合和时变时滞耦合的复杂网络，研究有噪声干扰下的均方簇同步问题．该网络所有耦合均为非线性，每一簇中节点动力学相同且不同簇节点动力学不同．通过引入Bernoulli随机变量，所有控制均以不同概率对该网络实施控制．根据Lyapunov稳定性理论和随机分析理论得到该网络实现均方簇同步的条件，并在理论上给出严格证明．数值实验证明所得理论正确．

英文摘要：

The mean square cluster synchronization is investigated in directed networks with non-identical nodes perturbed by communication noise as well as those with both delay and non-delay coupling. In addition, all node states in coupling processes are nonlinear with equal dynamic for nodes in a cluster but different dynamics for nodes in different clusters. The pinning control method is employed in designing controllers for guaranteeing cluster synchronization. All the controllers are supposed to occur with different probabilities by introducing Bernoulli stochastic variables. Some sufficient mean square synchronization conditions are derived and proved theoretically based on the Lyapunov stability theorem and the stochastic analysis theory. The theoretical results are verified by a numerical siinulation.