A theory for synchronization of dynamical systems |
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| Authors: | Albert CJ Luo |
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| Institution: | 1. Tianjin Key Laboratory of Advanced Technology of Electrical Engineering and Energy, School of Electrical Engineering and Automation, Tianjin Polytechnic University, Tianjin 300387, China;2. School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin 300387, China;1. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam;2. Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875–4413, Iran;3. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, GR–54124, Greece;4. Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90–924 Lodz, Poland |
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| Abstract: | In this paper, a theory for synchronization of multiple dynamical systems under specific constraints is developed from a theory of discontinuous dynamical systems. The concepts on synchronization of two or more dynamical systems to specific constraints are presented. The synchronization, desynchronization and penetration of multiple dynamical systems to multiple specified constraints are discussed, and the necessary and sufficient conditions for such synchronicity are developed. The synchronicity of two dynamical systems to a single specific constraint and to multiple specific constraints is investigated. Finally, the synchronization and the corresponding complexity for multiple slave systems with multiple master systems are discussed briefly. The meaning of synchronization for dynamical systems with constraints is extended as a generalized, universal concept. The theory presented in this paper may be as a universal theory for dynamical systems. The paper provides a theoretic frame work in order to control slave systems which can be synchronized with master systems through specific constraints in a general sense. |
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