Global dissipativity of non-autonomous BAM neural networks with mixed time-varying delays and discontinuous activations

In this paper, we investigate the dissipativity of a class of BAM neural networks with both time-varying and distributed delays, as well as discontinuous activations. First, the concept of the Filippov solution is extended to functional differential equations with discontinuous right-hand sides via functional differential inclusions. Then, by constructing Lyapunov functional and employing a generalized Halanay inequality, several sufficient easy-to-test conditions are successfully obtained to guarantee the global dissipativity of the Filippov solution of the considered system. The derived results extend and improve some previous publications on conventional BAM neural networks. Meanwhile, the estimations of the positive invariant and globally attractive set are given. Finally, numerical simulations are provided to demonstrate the effectiveness of our proposed results.

Finite-time synchronization problem of a class of discontinuous Cohen–Grossberg neural networks with mixed delays via new switching design

This paper investigates a class of generalized Cohen–Grossberg neural networks (CGNNs) with discontinuous activations and mixed delays. Based on the nonsmooth analysis theory, the drive-response concept, differential inclusions theory, we give several basic assumptions to gain the finite-time synchronization issue of CGNNs. Sufficient conditions are provided without the boundedness or monotonicity of discontinuous activation functions. Moreover, one can estimate the settling time’s upper bounds of the system. At last, two numerical examples and their simulations are given to further show the benefits of the obtained control approach.

Fixed-Time Synchronization of Delayed Memristive Neural Networks with Discontinuous Activations

In this paper, the fixed-time synchronization problem for a class of memristive neural networks with discontinuous neuron activation functions and mixed time-varying delays is investigated. With the help of the fixed-time stability theory, under the framework of Filippov solution and differential inclusion theory, several new and useful sufficient criteria for fixed-time synchronization are obtained by designing two types of energy-saving and simple controllers for the considered systems. Compared with the traditional fixed-time synchronization controller, the controllers used in this paper only have one power exponent term, which is a function of the system state error rather than a constant. Moreover, some previous relevant works are especially improved. Finally, two numerical examples are given to show the correctness and the effectiveness of the obtained theoretical results.