Event-triggered Impulsive Synchronization Of Fractional-order Coupled Neural Networks

As a special kind of neural networks,fractional-order coupled neural networks not only have the structure and function of neural networks,but also exhibit many complex dynamics.Because of its special structure,coupled neural networks have many applications in real life,such as information processing,security communication,pattern recognition and biological systems.Because fractional calculus has infinite memory and heritability,fractional mathematical model can better present some complex features in real system.Although some preliminary achievements have been made in this field,systematic theoretical research is still lacking in some aspects.Therefore,this thesis studies the synchronization problem of fractional-order coupled neural networks.The main contents are as follows:The first chapter introduces the background knowledge of coupled neural networks,fractional order,synchronization,event-triggered impulsive control and cyber attacks.The second chapter investigates the synchronization problem of fractional-order neural networks with coupling via event-triggered impulsive control.First,an eventtriggered impulsive control law based on state information is constructed to reduce network load and save computing resources.Impulsive control is active at impulsive instants determined by certain prespecified triggering functions,otherwise linear feedback control that is updated only at triggering instants is applied.Then,the su cient conditions for event-triggered impulsive synchronization of fractional-order coupled neural networks are derived and the e?ect of fractional order on synchronization rate is disvi cussed by using fractional Lyapunov theory,Kronecker product,comparison principle and Laplace transform.In addition,it has been proved that the designed event-triggered mechanism does not exist Zeno behavior.Finally,a typical chaotic system is simulated to verify the feasibility of the proposed event-triggered impulsive control technique and the correctness of the obtained results.The third chapter investigates the synchronization control issue of fractional-order fuzzy neural networks with nonlinear coupling strength under stochastic network attacks.First,two common types of cyber attacks are considered: denial of service attack and deception attack.By using two random independent Bernoulli variables,a mathematical model of random cyber attacks is established.Then,an event-triggered mechanism based on state errors is proposed to generate impulsive instants,that is,impulsive control is implemented at triggering instants.By applying fractional Lyapunov stability and fuzzy set theory,the su cient conditions are derived to guarantee event-triggered impulsive synchronization of fractional-order coupled fuzzy neural network under deception attacks and denial of service attacks.In addition,there exists a positive constant less than the time interval between arbitrary two consecutive impulsive instants,which means the Zeno phenomenon is eliminated.On this basis,an improved event-triggered control mechanism based on sampled data is constructed by utilizing the positive constant to further reduce information transmission.Finally,the feasibility and superiority of the theoretical results are illustrated by simulating and comparing the two examples.The fourth chapter summarizes the main work of this thesis and discusses the shortcomings of this thesis and the next research direction.