Pinning control of complex networks with time-varying inner and outer coupling

Hai Lin; Jingcheng Wang; Hai Lin; Jingcheng Wang

doi:10.3934/mbe.2021172

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 4: 3435-3447. doi: 10.3934/mbe.2021172

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Research article

Pinning control of complex networks with time-varying inner and outer coupling

Hai Lin ^1,3,
Jingcheng Wang ^{1,2,3
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1.
Key Laboratory of System Control and Information Processing, Ministry of Education of China, Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China
2.
Autonomous Systems and Intelligent Control International Joint Research Center, Xi’an Technological University, Xi’an 710021, China
3.
Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai 200240, China

Received: 25 January 2021 Accepted: 08 April 2021 Published: 19 April 2021

This paper addresses the pinning synchronization of nonlinear multiple time-varying coupling complex networks. Time-varying inner coupling in the single node state space and time-varying outer coupling among nodes in an entire complex network are taken into consideration. The main contribution is to propose some pinning synchronization criterion by which time-varying complex networks can be synchronized to the desired state. Besides, different parameters of linear controllers, adaptive controllers and adaptive coupling strength on the synchronization have been investigated. It is found that complex networks can achieve global synchronization by adaptively adjusting the coupling strength or controllers. Finally, simulation examples of random networks are given to verify the theoretical results.
- complex networks,
- time-varying coupling,
- pinning,
- global synchronization
Citation: Hai Lin, Jingcheng Wang. Pinning control of complex networks with time-varying inner and outer coupling[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3435-3447. doi: 10.3934/mbe.2021172

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Abstract

This paper addresses the pinning synchronization of nonlinear multiple time-varying coupling complex networks. Time-varying inner coupling in the single node state space and time-varying outer coupling among nodes in an entire complex network are taken into consideration. The main contribution is to propose some pinning synchronization criterion by which time-varying complex networks can be synchronized to the desired state. Besides, different parameters of linear controllers, adaptive controllers and adaptive coupling strength on the synchronization have been investigated. It is found that complex networks can achieve global synchronization by adaptively adjusting the coupling strength or controllers. Finally, simulation examples of random networks are given to verify the theoretical results.

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