Desynchronization in synchronous multi-coupled chaotic neurons by mix-adaptive feedback control

Abstract

In this paper, by means of the invariance principle of differential equations, an adaptive feedback scheme is proposed to realize desynchronization in synchronous multi-coupled chaotic neurons by the mix-adaptive feedback effectively. Numerical simulations for the Hindmarsh–Rose neural model with self-coupling are illustrated which agree well with our theoretical analysis. It is observed that the feedback strengths asymptotically converge to a local fixed value in finite time, especially for linear coupling chaotic neurons with self-coupling. Furthermore, robustness of desynchronization in three coupled chaotic neurons on small mismatch of parameters is shown.

Keywords:

• desynchronization
• adaptive delay feedback
• neural activity
• synaptic coupling strengths
• neuronal network
• feedback strength

2000 Mathematics Subject Classifications:

• 92B20
• 93C40

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants No. 10972018 and No. 11072013. This work is also partially supported by UTPA Faculty Council Grant under 145MATH04. Authors thank Dr Xiaohui Wang for providing us with the drawing technique.