Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2686-6
Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks∗ Shuang LIU1 , Runze ZHANG1 , Qingyun WANG2,† ,
Xiaoyan HE3
1. Shanghai Engineering Research Center of Physical Vapor Deposition Superhard Coating and Equipment, Shanghai Institute of Technology, Shanghai 201418, China; 2. Department of Dynamics and Control, Beihang University, Beijing 100191, China; 3. Department of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Huhhot 010070, China (Received Jun. 29, 2020 / Revised Aug. 12, 2020)
Abstract Based on the topological characteristics of small-world networks, a nonlinear sliding mode controller is designed to minimize the effects of internal parameter uncertainties. To qualify the effects of uncertain parameters in the response networks, some effective recognition rates are designed so as to achieve a steady value in the extremely fast simulation time period. Meanwhile, the Fisher-Kolmogorov and Burgers spatiotemporal chaotic systems are selected as the network nodes for constructing a drive and a response network, respectively. The simulation results confirm that the developed sliding mode could realize the effective synchronization problem between the spatiotemporal networks, and the outer synchronization is still achieved timely even when the connection probability of the small-world networks changes. Key words identification
synchronization, sliding mode control, small-world network, parameter
Chinese Library Classification O415.5 2010 Mathematics Subject Classification
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93C83, 93D05
Introduction
Synchronization has attracted significant attention in the last decade because of its extensive practical applications such as robot control, metabolic pathway, and aircraft formation. In a typical synchronous system, the data should be received and transmitted at the same time. It is crucial to ensure fast and reliable synchronous transmission, especially when a large number of data need to be transferred quickly. In 1990, the synchronization of coupled chaotic systems was ∗ Citation: LIU, S., ZHANG, R. Z., WANG, Q. Y., and HE, X. Y. Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2686-6 † Corresponding author, E-mail: [email protected] Project supported by the National Natural Science Foundation of China (Nos. 11602146, 11872304, and 11962019), the Science Foundation of Shanghai (No. 18ZR1438200), and the Chen Guang Project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation (No. 16CG65) c
The Author(s) 2020
2
Shuang LIU, Runze ZHANG, Qingyun WANG, and Xiaoyan HE
realized by using ordinary signals of negative Lyapunov exponents[1] . Since then, synchronization has become a fundamental subfield of nonlinear dynamics, and many theoretical and trial
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