Passivity And Synchronization Of Multi-weight Fractional-order Coupled Neural Network

The dynamical behaviors of coupled neural networks(passivity,synchronization,stability,dissipativity,etc.)have been widely explored and studied,which can not only help people better understand the dynamic characteristics of neural networks,but also help to fully utilize these dynamic characteristics in model identification,parallel computing and combinatorial optimization.On one hand,passivity,as a special dissipativity case,is an important aspect for people to study the dynamic characteristics of coupled neural networks,and synchronization and passivity are inextricably related,so it is important to explore passivity and ensure coupled neural networks to realize synchronization based on the passivity.In addition,considering that the nodes in a coupled neural network may be affected by the state of neighboring nodes or the rate of change of the state of neighboring nodes,state coupling and derivative coupling also become an important research element of coupled neural networks.On the other hand,since coupled neural networks need to achieve passivity and synchronization within finite time in some practical applications,finite-time passivity and finite-time synchronization have also gradually attracted the attention of researchers,and the authors in related fields have found that finite-time synchronization has the advantages of robustness against uncertainties and faster convergence,which indicates that the finite-time passivity and the finite-time synchronization have more important research meaning.Fractional calculus,as an important branch of calculus,has been applied in various fields including system identification,thermal system problems,control and machine problems,and so on.In fact,fractional-order calculus has excellent genetic and memory properties.In view of these advantages,coupled neural network modeling by fractional-order calculus will make the neural network model more accurate and effective,which is not available in the previously studied integer-order differential systems.This paper focuses on the passivity and passivity-based synchronization problems of coupled fractional-order neural networks with multi-state couplings and multi-derivative couplings.The passivity and synchronization criteria of coupled fractional-order neural networks with multiple state couplings are established.A model of coupled fractionalorder neural networks with multiple derivative couplings is developed,and several passivity and synchronization conditions are also derived.On the other hand,the finitetime passivity and finite-time synchronization problems of coupled fractional-order coupled neural networks with multiple state couplings and multiple derivative couplings are investigated,respectively.The finite-time passivity and finite-time synchronization of multiple state coupled and multiple derivative coupled fractional-order coupled neural networks are analyzed by using a state feedback control strategy.