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This paper is concerned with the dissipativity and synchronization problems of a class of delayed bidirectional associative memory (BAM) neural networks in which neuron activations are modeled by discontinuous bivariate functions. First, the concept of the Filippov solution is extended to functional differential equations with discontinuous right-hand sides and mixed delays via functional differential inclusions. The global dissipativity of the Filippov solution to the considered BAM neural networks is proven using generalized Halanay inequalities and matrix measure approaches. Second, to realize global exponential complete synchronization of BAM neural networks with multivariate discontinuous activations, discontinuous state feedback controllers are designed using functional differential inclusions theory and nonsmooth analysis theory with generalized Lyapunov functional method. Finally, several numerical examples are provided to demonstrate the applicability and effectiveness of our proposed results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the possibility to implement the periodic synchronization control of memristive neural networks with time-varying delay. On the one hand, we apply a new method based on Kakutani׳s fixed point theorem of set-valued maps to obtain the existence of periodic solutions for memristive neural networks. On the other hand, by designing novel discontinuous state-feedback controller and introducing some new analytic techniques, the drive–response structure of memristor-based neural networks with periodic coefficients can realize the p -type exponential complete synchronization. Moreover, the estimated rate of exponential synchronization depends on the time delay and system parameters. The analysis in this paper is performed via functional differential inclusions following the Filippov theory. Finally, the proposed design method and theoretical results are verified by numerical example with MATLAB programming. [ABSTRACT FROM AUTHOR]