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.

Novel Criteria of ISS Analysis for Delayed Memristive Simplified Cohen–Grossberg BAM Neural Networks

The memristor as the fourth circuit element, it can capture some key aspects of biological synaptic plasticity. So, it is significant that the characteristic of memristors is considered in neural networks. This paper investigates input-to-state stability (ISS) of a class of memristive simplified Cohen–Grossberg bidirectional associative memory (BAM) neural networks with variable time delays. In the sense of Filippov solution, some novel sufficient criteria for ISS are obtained based on differential inclusions and differential inequalities; when the input is zero, the stability of the total system is state stable. Furthermore, numerical simulations are illustrated to show the feasibility of our results.

Dynamical behaviors of the generalized hematopoiesis model with discontinuous harvesting terms

This paper is concerned with the generalized hematopoiesis model with discontinuous harvesting terms. Under the framework of Filippov solution, by means of the differential inclusions and the topological degree theory in set-valued analysis, we have established the existence of the bounded positive periodic solutions for the addressed models. After that, based on the nonsmooth analysis theory with Lyapunov-like approach, we employ a novel argument and derive some new criteria on the uniqueness, global exponential stability of the addressed models and convergence of the corresponding autonomous case of the addressed models. Our results extend previous works on hematopoiesis model to the discontinuous harvesting terms and some corresponding results in the literature can be enriched and extended. In addition, typical examples with numerical simulations are given to illustrate the feasibility and validity of obtained results.

Almost Periodic Dynamics of a Class of Delayed Neural Networks with Discontinuous Activations

We use the concept of the Filippov solution to study the dynamics of a class of delayed dynamical systems with discontinuous right-hand side, which contains the widely studied delayed neural network models with almost periodic self-inhibitions, interconnection weights, and external inputs. We prove that diagonal-dominant conditions can guarantee the existence and uniqueness of an almost periodic solution, as well as its global exponential stability. As special cases, we derive a series of results on the dynamics of delayed dynamical systems with discontinuous activations and periodic coefficients or constant coefficients, respectively. From the proof of the existence and uniqueness of the solution, we prove that the solution of a delayed dynamical system with high-slope activations approximates to the Filippov solution of the dynamical system with discontinuous activations.