Dynamic Behavior Analysis For A Class Of Memristive Inertial Neural Networks With Time Delay

This paper investigates the dynamics for a class of memristor-based inertial neural networks,which include dissipation,robust dissipation,finite-time synchronization,exponential synchronization and fixed-time synchronization.Firstly,based on non-reduction method,we use the Lyapunov stability theory to directly analyze the memristive inertial neural network,and some sufficient criterias are obtained to ensure its dissipation and robust dissipation.Secondly,the finite-time synchronization of the memristor-based inertial neural network drive-response system is achieved by designing a new state-feedback controller.It is worth pointing out(It should be noted)that the second-order system is reduced to the first-order differential equations through variable substitution,we find that there is a certain correlation between variable substitution and control gains.Further,we obtain the relatively optimal transformation and relatively optimal control gains,which effectively reduces the control cost in engineering applications.Again,we add a coupling term to the memristive inertial neural network for large-scale computation and practical application,and get some sufficient conditions that,respectively,exponential synchronization and fixed time synchronization of the coupled memristive inertial neural network.It update the related theorems of memristive inertial neural networks with coupling term.Finally,some examples to further verify and demonstrate the validity of the results obtained.