Research On Synchronization And State Estimation Of Several Classes Of Complex-Valued Neural Networks With Time Delays

Research related to neural networks has attracted lots of interest all over the world on account of various applications of neural networks in many fields,such as signal transmission,associative memory,pattern recognition,image processing,confidential communication,optimization calculation and so on.Among those mathematical models of neural networks,complex-valued neural networks can directly process complex-valued data due to the state,output and network weights of its neurons are complex values,which is natural and convenient.Fractional calculus can be regarded as the generalization of classical calculus from integer order to arbitrary order.In recent years,many scholars have investigated dynamic behaviors of fractional order neural networks owing to the advantages of memory and heredity of the fractional calculus description model.Besides,time delay always make system instability.Therefore,it is of great significance to study the synchronization and state estimation of complex-value neural networks with time delays.The main highlights in this paper are contained as follows:1.Global ?-synchronization of impulsive complex-valued neural networks with leakage delay and mixed time-varying delaysThe problem on synchronization is investigated for a class of impulsive complexvalued neural networks with discrete and distributed time-varying delays as well as leakage delay.By constructing appropriate Lyapunov-Krasovskii functional,and using Newton-Leibniz formulation,inequality technique and free-weighting matrix method,several sufficient criteria to guarantee the global ?-synchronization are derived for the considered impulsive complex-valued neural networks.The provided conditions are expressed in terms of linear matrix inequalities(LMI).An example with simulations is provided to verify the effectiveness of the obtained results.2.Robust state estimation for fractional-order complex-valued delayed neural networks with interval parameter uncertaintiesWithout separating complex-valued neural networks into two real-valued systems,the state estimation of fractional-order complex-valued neural networks(FCNNs)with uncertain parameters and time delay is investigated in this paper.Based on Lyapunov-Krasovskii functional approach,a new LMI criterion is derived for asymptotic stability of the estimation error system.A numerical example with simulations is given to confirm the feasibility and availability of the raised result.3.Synchronization of two nonidentical fractional-order complex-valued neural networks with leakage delay and time-varying delayWithout separating complex-valued neural networks into two real-valued systems,the synchronization of FCNNs with leakage delay and time-varying delay is studied via sliding mode control approach.By employing the fractional order Razumikhin theorem,a sufficient condition is derived to realize synchronization of the considered model.