Finite-time Mittag—Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay

Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks (FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag—Leffler synchronization (FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time (SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly, some simulation examples are designed to verify the validity of conclusions.     

融合STDP规则的忆阻联想记忆电路

脉冲时序依赖可塑性规则和联想记忆规则共同描述了神经元突触的可塑性,对生物的学习和遗忘有重要的影响。现有的脉冲时序依赖可塑性规则与忆阻器结合的相关研究,仅实现了联想记忆的学习功能。基于此,融合脉冲时序依赖可塑性规则设计了一种新的忆阻联想记忆电路。首先,分析脉冲时序依赖可塑性规则和联想记忆规则之间的联系;接着,设计一种具备延时功能的模块,融合两种规则;进一步,结合模块设计了一种忆阻联想记忆电路,实现了学习和三种遗忘功能;最后,通过PSPICE仿真验证了学习和三种遗忘功能,以及所提出方案的有效性。     

Finite-time Mittag-Leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions

The finite-time Mittag-Leffler synchronization is investigated for fractional-order delayed memristive neural networks(FDMNN)with parameters uncertainty and discontinuous activation functions.The relevant results are obtained under the framework of Filippov for such systems.Firstly,the novel feedback controller,which includes the discontinuous functions and time delays,is proposed to investigate such systems.Secondly,the conditions on finite-time Mittag-Leffler synchronization of FDMNN are established according to the properties of fractional-order calculus and inequality analysis technique.At the same time,the upper bound of the settling time for Mittag-Leffler synchronization is accurately estimated.In addition,by selecting the appropriate parameters of the designed controller and utilizing the comparison theorem for fractional-order systems,the global asymptotic synchronization is achieved as a corollary.Finally,a numerical example is given to indicate the correctness of the obtained conclusions.