Research Of Synchronization For Semi-markovian Jumping Discontinuous Complex Networks

Neural networks(NNs)and complex dynamical networks(CDNs)are important research fields in system science,among them,the synchronization issue for neural networks and complex dynamical networks is one of the hot issues for scholars to study.In this paper,the synchronization issue for neural networks and discontinuous complex dynamical networks with semi-Markovian jumping is studied.The following is the main contents of this paper:Firstly,based on the introduction of Lyapunov-Krasovskii functional,the fixed-time synchronization issue for semi-Markovian jumping neural networks is investigated.By designing a novel state feedback controller,and applying a series of inequality techniques,the sufficient conditions of fixed-time synchronization for neural networks with semi-Markovian jumping are given,and the setting time of synchronization is also estimated.Secondly,by using the properties of semi-Markovian switching system,the global finitetime and fixed-time synchronization issue for discontinuous complex networks with semiMarkovian switching is investigated.By designing a state feedback controller with integral terms and time-varying delay terms,applying stochastic analysis theory and nonsmooth analysis theory,the sufficient criteria of global finite-time and fixed-time synchronization for discontinuous complex networks are obtained,and the upper bound of setting time of synchronization is estimated accurately.Finally,by introducing the semi-Markovian stochastic process,the stochastic finite-time synchronization issue for discontinuous complex dynamical networks with nonidentical nodes and noise disturbance is discussed.Under the Filippov differential inclusion framework,the sufficient conditions of stochastic finite-time synchronization are obtained by designing appropriate Lyapunov-Krasovskii functional.