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In this study, the cluster synchronisation problem of Lur'e networks is focused with non-linear coupling. There are both identical and non-identical nodes in the dynamical system and the coupling matrix is asymmetrical. By using the linear and non-linear negative feedback control schemes, the Lyapunov stability theorem and linear matrix inequality, sufficient conditions are obtained that guarantee the realisation of the cluster synchronisation pattern for all initial values. Numerical simulation results are also given to support the validity of the main results.

This paper is concerned with the exponential synchronization issue of nonidentically coupled neural networks with time-varying delay. Due to the parameter mismatch phenomena existed in neural networks, the problem of quasi-synchronization is thus discussed by applying some impulsive control strategies. Based on the definition of average impulsive interval and the extended comparison principle for impulsive systems, some criteria for achieving the quasi-synchronization of neural networks are derived. More extensive ranges of impulsive effects are discussed so that impulse could either play an effective role or play an adverse role in the final network synchronization. In addition, according to the extended formula for the variation of parameters with time-varying delay, precisely exponential convergence rates and quasi-synchronization errors are obtained, respectively, in view of different types impulsive effects. Finally, some numerical simulations with different types of impulsive effects are presented to illustrate the effectiveness of theoretical analysis.

In this article, the mean square exponential synchronization of a class of impulsive coupled neural networks with time-varying delays and stochastic disturbances is investigated. The information transmission among the systems can be directed and lagged, that is, the coupling matrices are not needed to be symmetrical and there exist interconnection delays. The dynamical behaviors of the networks can be both continuous and discrete. Specially, the timevarying delays are taken into consideration to describe the impulsive effects of the system. The control objective is that the trajectories of the salve system by designing suitable control schemes track the trajectories of the master system with impulsive effects. Consequently, sufficient criteria for guaranteeing the mean square exponential convergence of the two systems are obtained in view of Lyapunov stability theory, comparison principle, and mathematical induction. Finally, a numerical simulation is presented to show the verification of the main results in this article.

This paper investigates the exponential synchronization of nonidentically coupled Lur'e dynamical networks with proportional delay. Since the heterogeneities existed in different Lur'e systems, quasi-synchronization rather than complete synchronization is thus discussed. Different from general time delay, the proportional delay is a type of unbounded time-varying delay, which tremendously increases the requirements on network synchronization. Based on distributed impulsive pinning control protocol and different roles that impulsive effects play, the criteria for quasi-synchronization of nonidentically coupled Lur'e dynamical networks are derived by jointly applying the delayed impulsive comparison principle, the extended formula for the variation of parameters, and the definition of an average impulsive interval. Moreover, synchronization errors for different impulsive effects with different functions are evaluated and simultaneously, the corresponding exponential convergence rates are obtained. In addition, three numerical examples are presented to illustrate the validity of the control scheme and the theoretical analysis.