Dissipativity analysis of stochastic memristor-based recurrent neural networks with discrete and distributed time-varying delays

ABSTRACT

In this paper, based on the knowledge of memristor-based recurrent neural networks (MRNNs), the model of the stochastic MRNNs with discrete and distributed delays is established. In real nervous systems and in the implementation of very large-scale integration (VLSI) circuits, noise is unavoidable, which leads to the stochastic model of the MRNNs. In this model, the delay interval is decomposed into two subintervals by using the tuning parameter α such that 0 < α < 1. By constructing proper Lyapunov–Krasovskii functional and employing direct delay decomposition technique, several sufficient conditions are given to guarantee the dissipativity and passivity of the stochastic MRNNs with discrete and distributed delays in the sense of Filippov solutions. Using the stochastic analysis theory and Itô’s formula for stochastic differential equations, we establish sufficient conditions for dissipativity criterion. The dissipativity and passivity conditions are presented in terms of linear matrix inequalities, which can be easily solved by using Matlab Tools. Finally, three numerical examples with simulations are presented to demonstrate the effectiveness of the theoretical results.

KEYWORDS:

• Dissipativity
• Filippov solution
• linear matrix inequalities
• memristor
• stochastic neural networks

Acknowledgements

The authors are very thankful to the editors and anonymous reviewers for their careful reading, constructive comments and fruitful suggestions to improve this article.

Funding

This work is supported by the University Grants Commission - Basic Science Research (UGC - BSR) Research fellowship in Mathematical Sciences - 2013–2014, Govt. of India, New Delhi.

Additional information

Funding

This work is supported by the University Grants Commission - Basic Science Research (UGC - BSR) Research fellowship in Mathematical Sciences - 2013–2014, Govt. of India, New Delhi.