The Investigation Of Collective Behaviors In Complex Delayed Dynamical Networks Via Discontinuous Control

The control of collective behaviors in complex delayed dynamical networks is a key part of the investigation and application of complex networks,and has an important theoretical value and practical significance.Owing to the fact that impulsive control and intermittent control these two discontinuous control techniques can save the control cost and be easily implemented in actual applications,the collective behaviors of complex dynamical networks under discontinuous control have attracted extensively attention in recent years.This thesis aims to study the discontinuous control problem for synchronization of three kinds of complex delayed dynamical networks,the research contents mainly include the following three aspects:Firstly,exponential cluster synchronization of a class of general delayed dynamical networks with hybrid coupling and impulsive effect is studied.Based on average impulsive interval approach and the analysis technique,some novel sufficient conditions for globally exponential cluster synchronization are established.It is indicated that the derived cluster synchronization criteria can be simultaneously applied to deal with the synchronization problem of general delayed dynamical networks with synchronizing impulses or desynchronizing impulses.Finally,numerical examples are provided to show the correctness of the theoretical results.Secondly,the problem of exponential synchronization of directed networks with complex-variable systems and distributed delays coupling is explored.An adaptive nonperiodical intermittent control scheme is adopted to realize exponential synchronization of the complex-variable directed delayed dynamical networks.By means of the complex inequality,piecewise analysis method and Lyapunov stability theory,some sufficient conditions are established to guarantee global exponential synchronization.In addition,the established synchronization criteria rely on the control rates instead of the control periods,and therefore,for practical problems,the control periods can be self-adjusted according to the criteria and the control widths.Finally,numerical simulations are given to illustrate the feasibility of the proposed control method.Finally,the pinning synchronization of memristor-based neural networks with time-varying delays via intermittent control is investigated.By applying nonperiodic intermittent control to partial nodes of the memristor-based delayed neural networks,some general criteria for globally exponential synchronization are derived based on the theories of differential inclusions and nonsmooth analysis.Additionally,a feasible region of the control gains and control rates is established for achieving globally exponential synchronization.Finally,the effectiveness of the theoretical analysis is verified via numerical simulations...