Impulsive synchronisation of linear complex dynamical networks with time delay on time scales

ABSTRACT

In this paper, we investigate the impulsive synchronisation of linear complex dynamical networks (CDNs) with time delay on time scales by a method of pinning impulsive control. We use the time scales theory and the Lyapunov method to derive a synchronisation criterion. We find that we can achieve the synchronisation of CDNs through only controlling a small number of nodes and the modelling framework here can enrich the models of continuous/discrete-time CDNs. In the end, we give some numerical simulations to demonstrate the feasibility of the theoretical analysis.

KEYWORDS:

• Synchronisation
• complex dynamical networks (CDNs)
• time scales
• pinning control

MSC:

• 34K20
• 34K13
• 92B20

Acknowledgments

The authors sincerely thank the anonymous reviewers for their careful reading, constructive comments and suggestions for improving the quality of the manuscript.

Disclosure statement

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

Additional information

Funding

This work was partially supported by the Natural Science Foundation of Shandong Province under Grant ZR2021MA043.