Stability And Synchronization Control Of Several Types Of Memristive Neural Networks

Memristors,characterized as a class of non-linear,retentive resistive devices encapsulating computational and memory capabilities,are ubiquitously recognized as optimal constituents for simulating human synaptic functionalities,owing to their nanometric dimensions,superior integrability,and extensive plasticity.In recent years,novel artificial neural networks based on memristors have rapidly developed.Compared to conventional neural networks,neural networks augmented by memristive components demonstrate superior capabilities in information storage and processing.Furthermore,they exhibit exceptional performance in various critical applications,including associative memory,pattern recognition,and brain-inspired computing.To satiate a diverse spectrum of practical requirements,this dissertation introduces elements such as stochastic noise,diffusion,and algebraic constraints into the memristive neural network model,aiming to enrich and optimize extant models.On the other hand,the dynamic behaviors intrinsic to the memristive neural network model,notably its stability and synchronization,have a decisive influence on its deployment in correlated disciplines.As a result,conducting a stability analysis on the improved memristive neural network model and formulating efficacious control strategies to facilitate synchronization are of paramount importance.An exhaustive exploration of the stability and synchronization of the memristive neural network model serves to not only foster a profound comprehension of the operational mechanics of the human cerebrum but also stimulate the continuous evolution and expansive application of memristive neural networks within the fields of neuromorphic computing and neurocognitive science.This dissertation focuses on the optimization of several types of memristive neural network models,with an emphasis on investigating their stability and synchronization control issues.Within the framework of Filippov’s solution,coupled with theories of stochastic analysis,fractional calculus,Lyapunov stability,and the design of a series of reasonable control strategies,sufficient conditions for the stability and synchronization of different types of memristive neural networks have been acquired,thus significantly enriching the dynamical theory of memristive neural networks.Following is a synopsis of the main content of this dissertation:1)Pinning synchronization of stochastic neutral reaction-diffusion memristive neural networks is investigated.The existing model is further optimized by introducing stochastic noise,diffusion,and neutral delay.On this basis,two innovative pinning controllers are designed,which simultaneously consider both the current and past states.With the aid of Green’s theorem,inequality techniques,stochastic analysis theory,and pinning control technology,new Lyapunov functionals are constructed to establish two sufficient conditions to ensure that the proposed memristive neural networks can achieve mean-square asymptotic synchronization.It is worth mentioning that this work advances some existing achievements.Finally,numerical simulations further verify the correctness and effectiveness of the obtained results.2)Asymptotic stability and synchronization of fractional delayed memristive neural networks with algebraic constraints,in the Riemann-Liouville sense,is investigated.For real circuits,fractional-order capacitance can offer a more precise portrayal of the dynamic behaviors of circuits.Consequently,the need to expand the memristive neural network model from integer-order to fractional-order has become particularly urgent.Firstly,fractional operator is introduced into the existing delayed memristive neural network,taking a deeper consideration of the impact of algebraic constraints on the model.This leads to the construction of a novel class of fractional singular delayed memristive neural networks model,and an analysis of its stability and synchronization control problems.Next,by employing the Lyapunov functional method,a criterion for the asymptotic stability of the system was obtained.Subsequently,a set of appropriate feedback and adaptive control schemes are designed to achieve synchronization of the study system,and two sufficient conditions are derived.The results of this study not only effectively address the challenges posed by delays and algebraic constraints,but the conclusions drawn are also more aligned with practical requirements.Finally,numerical simulations further verify the correctness and effectiveness of the research results.3)Stability and pinning synchronization of fractional delayed reaction-diffusion memristive neural networks in the Riemann-Liouville sense is investigated.Initially,diffusion factor is introduced into existing fractional delayed memristive neural network models.Then,by combining the Green’s theorem and inequality techniques,a relatively non-conservative criterion for the asymptotic stability of the system is provided through the Lyapunov direct method.Further,by designing appropriate pinning feedback controllers and adaptive controllers,synchronization of the proposed system is achieved,and two suficient conditions for global asymptotic synchronization are determined.Finally,numerical simulations further confirm the validity of the conclusions.4)Stability of fractional nonlinear neutral systems is investigated,with an exploration of its applications in memristive neural networks.The LyapunovKrasovskii direct method,as a significant stability analysis too,is widely applied in researching the stability of Riemann-Liouville fractional nonlinear neutral systems.However,existing literature has constructed some debatable Lyapunov functionals.Therefore,a modification is proposed and applied to the stability and synchronization analysis of fractional neutral memristive neural networks.Initially,a novel,revised Lyapunov functional construction scheme is presented,leading to sufficient condition for the asymptotic stability of fractional nonlinear neutral systems.Subsequently,based on the aforementioned result,a relatively non-conservative algebraic inequality criterion for the asymptotic stability of fractional neutral memristive neural networks is derived.Concurrently,novel feedback and adaptive control schemes are designed to synchronize the proposed memristive neural networks,establishing two sufficient conditions for global asymptotic synchronization.Lastly,numerical simulations further confirm the correctness and effectiveness of the conclusions.5)Pinning synchronization of fractional neutral-type reaction-diffusion memristor-based neural networks is investigated.Firstly,the diffusion is introduced into the Riemann-Liouville fractional neutral memristive neural network model.Subsequently,two novel pinning controllers considering both the current and past states are designed.Next,with the aid of Green’s theorem,inequality techniques,and pinning control techniques,a new modified Lyapunov functional is proposed,which enables to obtain two less conservative criteria to ensure the asymptotic synchronization of the researched system.In addition,the conclusions based on algebraic inequalities have corrected and improved some existing results.Finally,numerical simulations validate the correctness of the conclusions obtained.