Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks

doi:10.1007/s10483-020-2686-6

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (12): 1833-1846.doi: 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

收稿日期:2020-06-29 修回日期:2020-08-12 发布日期:2020-11-21
通讯作者: Qingyun WANG E-mail:nmqingyun@163.com
基金资助:
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)

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:2020-06-29 Revised:2020-08-12 Published:2020-11-21
Contact: Qingyun WANG E-mail:nmqingyun@163.com
Supported by:
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)

摘要/Abstract

摘要： 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.

关键词: synchronization, sliding mode control, small-world network, parameter identification

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: synchronization, sliding mode control, small-world network, parameter identification

中图分类号:

93C83
93D05

Shuang LIU, Runze ZHANG, Qingyun WANG, Xiaoyan HE. Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(12): 1833-1846.

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Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks

Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks

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