Research On Synchronization Of Memristor-based Neural Networks

This paper mainly focuses on the finite-time synchronization and the fixed-time synchronization of memristor-based neural networks.Due to the discontinuity of the memristive weight coefficients,the right side of neural network system is discontinuous so that it does not have the solution in the classical sense.Applying the differential inclusion and the set-valued mapping theorems,we consider the solutions in the sense of Filippov.This paper mainly consists of three parts:Firstly,the fixed-time synchronization problem of memristor-based neural networks with impulsive effects and time-varying delays is considered.Design suitable controllers and Lyapunov functions,and calculate the impulse points and non-pulse points respectively.Then the error between the response-drive systems can be stabilized within a fixed time.That is,the fixed-time synchronization is achieved between the response system and the drive system.Meanwhile,an effective estimation for the upper bound of the time is made so that the synchronization can be achieved.Secondly,based on the fractional-order memristor-based neural network model in the complex-valued field,its finite-time projective synchronization is analyzed.The real and imaginary parts of the complex-valued system are split into two real systems,and the Caputo fractional derivative is selected.Design suitable controllers and Lyapunov functions together with the Gronwall-Bellman integral inequality and the Mittag-Leffler stability theorem.Finally,the sufficient conditions for the fractional-order complex-valued memristor-based neural networks to achieve the finite-time projective synchronization are obtained.We also estimate the upper bound of the time required for the drive system and the response system to reach the synchronization.Thirdly,the fixed-time synchronization of complex-valued memristor-based neural networks with impulsive effects is studied.The complex-valued memristorbased neural networks are separated into real systems,then the appropriate Lyapunov function and the controller are designed.Due to the discontinuity of the systemcaused by the impulse points,we construct the comparison system and segment it.Thus,the sufficient condition for the systems to achieve the fixed-time synchronization is deduced,we also give the upper bound of the time to achieve the fixed-time synchronization.Finally,the validity and correctness of the theoretical results are verified by examples and numerical simulations.