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.

Global dissipativity and finite-time synchronization of mixed time-varying delayed memristor-based neural networks with discontinuous activations

In this paper, the matters of dissipativity and finite time synchronization for memristor-based neural networks (MNNs) with mixed time-varying discontinuities are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. Then, the global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, some novel sufficient conditions are introduced to guarantee the finite-time synchronization of the drive-response MNNs based on a simple Lyapunov function and two different feedback controllers. Finally, several numerical examples are given to verify the validity of the theoretical results.

Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations

In this paper, the matters of dissipativity and synchronization for non-autonomous Hopfield neural networks with discontinuous activations are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. The global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, the global exponential synchronization of the addressed network drive system and the response system is realized by utilizing inequality and some analysis techniques and designing the discontinuous state feedback controller. Finally, several numerical examples are given to verify the validity of the theoretical results.

Polynomial dissipativity of proportional delayed BAM neural networks

This paper pays close attention to the global polynomial dissipativity (GPD) for proportional delayed BAM neural networks (PDBAMNNs). The global exponential dissipativity (GED) and the global dissipativity (GD) are also talked about. Under the help of novel Lyapunov functionals and a generalized Halanay inequality, a set of dissipative criteria for such systems are led out, together with the global polynomial attracting set (GPAS) and the global attracting set (GAS). Further, the relationship among GPD, GED and GD is unveiled. Finally, a proposed theoretical condition is validated through a simulation experiment.

Lag Synchronization Criteria for Memristor-Based Coupled Neural Networks via Parameter Mismatches Analysis Approach

This letter focuses on lag synchronization control analysis for memristor-based coupled neural networks with parameter mismatches. Due to the parameter mismatches, lag complete synchronization in general cannot be achieved. First, based on the [Formula: see text]-measure method, generalized Halanay inequality, together with control algorithms, some sufficient conditions are obtained to ensure that coupled memristor-based neural networks are in a state of lag synchronization with an error. Moreover, the error level is estimated. Second, we show that memristor-based coupled neural networks with parameter mismatches can reach lag complete synchronization under a discontinuous controller. Finally, two examples are given to illustrate the effectiveness of the proposed criteria and well support theoretical results.

Input-to-State Stability of Singularly Perturbed Control Systems with Delays

We study the input-to-state stability of singularly perturbed control systems with delays. By using the generalized Halanay inequality and Lyapunov functions, we derive the input-to-state stability of some classes of linear and nonlinear singularly perturbed control systems with delays.

NUMERICAL AND ANALYTIC DISSIPATIVITY OF THE θ-METHOD FOR DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED VARIABLE LAG

This paper focuses on the analytic and numerical dissipativity of θ-method for delay differential equations with a bounded variable lag. A generalized Halanay inequality is derived, and a sufficient condition is presented to ensure that delay differential equations with a bounded variable lag are dissipative. We then apply θ-method to such delay differential equations, and investigate the numerical dissipativity of the θ-method.