Non-periodically intermittent exponential synchronization of fractional-order multi-links complex dynamical networks

Abstract

In this paper, the exponential synchronization of fractional-order multi-links complex dynamical networks (CDNs) is studied based on non-periodically intermittent control. By means of the Lyapunov method and graph-theoretic approach, a Lyapunov-type theorem is provided based on the existence of vertex-Lyapunov functions. Then by giving the specific vertex-Lyapunov functions, a coefficients-type theorem is presented where the conditions of it are based on the coefficients of system. Moreover, to show the practicality of theoretical results, we give two applications to fractional-order chaotic CDNs with multiple links and fractional-order Hindmarsh–Rose neuron systems with multiple links, respectively. Meanwhile, two numerical examples are given to demonstrate the validity and feasibility of the theoretical results.

Keywords:

• Fractional-order
• complex dynamical networks
• exponential synchronization
• non-periodically intermittent control

AMS Subject Classifications:

• 34A08
• 34D06
• 05C82
• 93B52

Acknowledgments

The authors really appreciate the valuable comments of the editors and reviewers.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Shandong Province Natural Science Foundation [grant numbers ZR2018MA005, ZR2018MA020, and ZR2017MA008]; the Key Project of Science and Technology of Weihai [grant number 2014DXGJMS08], the Innovation Technology Funding Project in Harbin Institute of Technology [grant number HIT.NSRIF.201703], the Science and Technology Program of Shenzhen, China [grant number JCYJ20170818091621856] and the National Science Foundation of China [grant number 61872429].