# Exponential synchronization of memristor-based recurrent neural networks with multi-proportional delays

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## Abstract

This paper focuses on the exponential synchronization of memristor-based recurrent neural networks with multi-proportional delays. Act as a vital mathematical model, the system with proportional delays has been widely popular in several scientific fields, such as biology, physics systems as well as control theory. In the sense of Filippov solutions, we receive a novel sufficient condition based on the theories of set-valued maps and differential inclusions, by constructing a proper Lyapunov functional and taking advantage of inequality techniques. Here, the condition is easy to be verified by algebraic methods. A couple of numerical examples and their simulations are given to illustrate the correctness and effectiveness of the obtained results.

## Keywords

Memristor-based neural networks Proportional delay Exponential synchronization Feedback control Lyapunov functional Filippov solution## Notes

### Acknowledgements

The work is supported by the National Science Foundation of China (No. 61374009), Project training of backbone teachers in colleges and universities of Tianjin (No. 043-135205GC38).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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