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

Abstract 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.

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Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2013.09.004 ◽

2014 ◽

Vol 19 (5) ◽

pp. 1279-1300 ◽

Cited By ~ 58

Author(s):

Zuowei Cai ◽

Lihong Huang

Keyword(s):

Neural Networks ◽

Differential Inclusions ◽

Time Varying ◽

Bam Neural Networks ◽

Dynamic Behaviors ◽

Functional Differential ◽

Functional Differential Inclusions

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Global exponential stability analysis of anti-periodic solutions of discontinuous bidirectional associative memory (BAM) neural networks with time-varying delays

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0220 ◽

2020 ◽

Vol 21 (7-8) ◽

pp. 807-820

Author(s):

Xiangying Fu ◽

Fanchao Kong

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Periodic Solutions ◽

Associative Memory ◽

Time Varying ◽

Bam Neural Networks ◽

Bidirectional Associative Memory ◽

Globally Exponential Stability ◽

Discontinuous Activations ◽

Neural Network System

AbstractThis paper is concerned with a class of bidirectional associative memory (BAM) neural networks with discontinuous activations and time-varying delays. Under the basic framework of differential inclusions theory, the existence result of solutions in sense of Filippov solution is firstly established by using the fundamental solution matrix of coefficients and inequality analysis technique. Also, the boundness of the solutions can be estimated. Secondly, based on the non-smooth Lyapunov-like approach and by construsting suitable Lyapunov–Krasovskii functionals, some new sufficient criteria are given to ascertain the globally exponential stability of the anti-periodic solutions for the proposed neural network system. Furthermore, we have collated our effort with some previous existing ones in the literatures and showed that it can take more advantages. Finally, two examples with numerical simulations are exploited to illustrate the correctness.

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

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-191397 ◽

2021 ◽

Vol 40 (1) ◽

pp. 1695-1712

Author(s):

Kaifang Fei ◽

Minghui Jiang ◽

Yadan Zhang

Keyword(s):

Neural Networks ◽

Finite Time ◽

Time Synchronization ◽

Sufficient Conditions ◽

Time Varying ◽

Matrix Measure ◽

Feedback Controllers ◽

Discontinuous Activations ◽

Inclusion Theory ◽

Generalized Halanay Inequality

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.

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

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0073 ◽

2020 ◽

Vol 21 (7-8) ◽

pp. 693-704 ◽

Cited By ~ 1

Author(s):

Kaifang Fei ◽

Minghui Jiang ◽

Meng Yan ◽

Weizhen Liu

Keyword(s):

Neural Networks ◽

State Feedback ◽

Exponential Synchronization ◽

Matrix Measure ◽

Analysis Techniques ◽

Discontinuous Activations ◽

Inclusion Theory ◽

Generalized Halanay Inequality ◽

New Criteria ◽

Theoretical Results

AbstractIn 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.

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