Adaptive Pinning Synchronization of Fractional Complex Networks with Impulses and Reaction–Diffusion Terms

Xudong Hai, Guojian Ren, Yongguang Yu and Conghui Xu
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Xudong Hai: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
Guojian Ren: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
Yongguang Yu: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
Conghui Xu: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China

Mathematics, 2019, vol. 7, issue 5, 1-17

Abstract: In this paper, a class of fractional complex networks with impulses and reaction–diffusion terms is introduced and studied. Meanwhile, a class of more general network structures is considered, which consists of an instant communication topology and a delayed communication topology. Based on the Lyapunov method and linear matrix inequality techniques, some sufficient criteria are obtained, ensuring adaptive pinning synchronization of the network under a designed adaptive control strategy. In addition, a pinning scheme is proposed, which shows that the nodes with delayed communication are good candidates for applying controllers. Finally, a numerical example is given to verify the validity of the main results.

Keywords: fractional complex networks; adaptive control; pinning synchronization; time-varying delays; impulses; reaction–diffusion terms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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