Research On The Dynamics Of Impulsive Memristive Neural Networks

As a component integrating storage and computing,the memristor can be used to simulate artificial synapse and construct the memristive neural networks(MNNs).The MNNs,which have complex dynamic characteristics,are expected to widely used in brain simulation,combinatorial optimization,pattern recognition and other applications.MNNs have garnered widespread attention from the scientific and engineering communities.At present,the establishment of more accurate mathematical models of MNNs,as well as the development of effective methods of analysis and control,continue to be important challenges in the research of MNNs dynamics.This dissertation takes the impulsive MNNs as the research object.The factors with parameter mismatch,stochastic disturbance,Markovian jumping and time delay are introduced to construct a more practical and more complex MNNs mathematical model.The control strategies such as event triggering and switching are adopted to establish sufficient criteria for its dynamic characteristics such as stabilization and synchronization.The main work is summarized in the following four parts.1.Aiming at the mismatch of state dependent memristive coefficients,a stochastic impulsive MNNs model with mismatched parameters is constructed,and the effective criteria of projective synchronization are obtained.First,the impulsive controllers with and without time delays are designed respectively.Simultaneously,the influence of stochastic disturbance is considered,making the system more complex and closer to the practical situation.Second,the augmented form of the master system and error system is employed to retain more system information and reduce conservatism.Then,the essential criteria for weak projective synchronization of the master-slave impulsive system are established by constructing Lyapunov functionals and using the It(?) formula and two types of comparison principles.Finally,a numerical simulation and an application simulation are applied to prove the effectiveness of the results.2.Aiming at the problem of impulsive signal redundancy,a hybrid control stochastic impulsive MNNs model is designed,and effective strategies of exponential synchronization are established.First,the mismatched parameters of the stochastic impulsive system are processed utilizing the theories of differential inclusions and set-valued maps,as well as the form of uncertain terms.Sencond,to minimize the controller's control cost and update frequency,a hybrid controller is adopted that incorporates the strategies of switching,quantization,and event triggering.Then,the Lyapunov functionals with integral terms are developed to deal with the delay term of the system,and the It(?) formula is utilized to handle the stochastic component,yielding the decision strategy for the exponential synchronization of the stochastic impulsive MNNs.Finally,the feasibility and effectiveness of the results are verified by a numerical simulation.3.Aiming at the cooperation problem of multiple network nodes,a stochastic coupled impulsive MNNs model is constructed,and the effective judgments of finite-time synchronization are proposed.First,the effects of stochastic disturbances caused by product noise and impulses with probabilistic time delay on the performance of the system are studied.Second,the method of using upper and lower bounds to determine the weight range is proposed to process the memristive connection weights and use the uncertain terms to meet their various requirements.It is more accurate than the binary technique regarding the actual change in connection weights.The system's coupling strength and impulse strength are mismatched and modifiable thanks to the T-S fuzzy rule,resulting in increased resilience and greater robustness.Then,by constructing Lyapunov functionals and using impulsive control theory,sufficient criteria for finite-time synchronization with synchronous and asynchronous impulses are established.Finally,a numerical simulation is used to verify the validity of the synchronization conditions.4.Aiming at the problem of information lock,a more universal Markovian jumping impulsive MNNs model is constructed,and the effective criteria of stability are presented.First,in order to save network bandwidth,an event-triggered control strategy with Markovian jumping parameters is designed.By constructing the Lyapunov functional with single integral and double integral,the stability criterion of the error system is obtained.Then,because network attacks often occur in the process of information transmission,Do S/spoofing attacks with a certain probability are considered.The T-S fuzzy rule is used to fuzzify the memristive weight of the system,so as to meet the richness of the memristive weight value.The sufficient conditions for the stability are established by selecting the appropriate Lyapunov functional.Finally,the effectiveness and superiority of the results are proved by a numerical simulation.