Stability Analysis And Synchronous Control Of Several Kinds Of Inertial Memristive Neural Networks

Memristor is a kind of nonlinear device,which is similar to the characteristics of biological brain synapses.It can effectively simulate the learning and memory functions of biological brain by using memristor as electronic synapse in neural networks.Inertia term is ubiquitous in real physical systems and often leads to systems have more complex dynamic performances.Then,it is helpful to expand the applications of neural networks to bring the inertia item into neural networks.Therefore,this paper will study the stability and synchronization of inertial memristive neural networks.The main research contents are listed as follows:Firstly,the global exponential stability of inertial Cohen-Grossberg memristive neural networks is studied.Without constructing the Lyapunov function,sufficient conditions of global exponential stability are obtained by means of matrix measures and Halanay inequalities.And the correctness of the main results are provided by numerical simulations.Secondly,adaptive synchronization of inertial memristive neural networks is investigated.Inertial memristive neural networks is transformed into a system with interval parameters based on Filippov solution and differential inclusion theory.And,with employing the appropriate Lyapunov function,a novel discontinuous adaptive controller is designed.The controller can effectively realize synchronization of the drive-response system of inertial memristive neural networks.In addition,numerical simulations are given out to show the effectiveness of the adaptive control strategy.Finally,finite-time/fixed-time coopetition synchronization of the coupled inertial memristive neural networks are addressed.Coopetition synchronization can be regarded as the promotion of synchronization and anti-synchronization.Firstly,the coopetition interaction networks are characterized by a signed graph.Meanwhile,some useful discontinuous controllers are established by constructing appropriate Lyapunov functions under the assumption of structural equilibrium.What's more,a virtual leader node is introduced as a reference signal.And,the sufficient conditions of finite-time/fixed-time coopetition synchronization are presented by employing the signed graph theory,inequality technology and finite-time control theory.At last,the effectiveness of established control schemes are verified by illustrative examples with simulations.