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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]

This paper investigates the issue of global exponential synchronization for a class of general neural networks that contains discontinuous activation functions and mixed time delays. Functional differential inclusions and nonsmooth analysis theories are used as bases to design discontinuous controllers, such that the discontinuous neural networks can be exponential complete synchronized. This novel approach and its applicability to neural networks with continuous activations are also easily verified. Several numerical examples demonstrate the practicality and effectiveness of the design method. [ABSTRACT FROM AUTHOR]