Pinning synchronization of fractional-order delayed complex networks with non-delayed and delayed couplings

ABSTRACT

This paper considers the global synchronization of fractional-order delayed complex networks with non-delayed and delayed couplings based on pinning control. With the help of comparison theorems for fractional-order linear systems with multiple time delays, some novel and useful synchronisation criteria are presented by adding linear error feedback controllers to certain selected nodes. Here, the coupling matrices need not be symmetric or irreducible. What is more, it is shown that the model and results in the paper are more general than those in the literature. A numerical example is given to demonstrate the effectiveness and feasibility of the obtained results.

KEYWORDS:

• Synchronisation
• fractional-order system
• complex network
• delay

Acknowledgment

The authors would like to thank the anonymous referees and the editor for their valuable comments and suggestions. This work was supported by the National Natural Science Funds of China (Nos. 61403115, 11571016, 51177035, 51577046), the State Key Program of National Natural Science Foundation of China (No. 51637004), the national key research and development plan ‘important scientific instruments and equipment development’ (No. 2016YFF0102200), the Natural Science Foundation of Anhui Province (No. 1508085QF120) and the Fundamental Research Funds for the Central Universities (Nos. JZ2016HGTB0718, JZ2016HGXJ0022).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Funds of China [Grant Numbers 61403115, 11571016, 51177035, 51577046]; the State Key Program of National Natural Science Foundation of China [Grant Number 51637004]; the National Key Research and Development Plan ‘important scientific instruments and equipment development’ [Grant Number 2016YFF0102200]; the Natural Science Foundation of Anhui Province [Grant Number 1508085QF120]; the Fundamental Research Funds for the Central Universities [Grant Numbers JZ2016HGTB0718, JZ2016HGXJ0022].