Generalized synchronization of strictly different systems: Partial-state synchrony |
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| Authors: | JG Barajas Ramírez KP Cuéllar Galarza R Femat |
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| Institution: | 1. Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of Korea;2. School of Electrical Engineering and Automation, Jiangsu Normal University, Xuzhou, Jiangsu 221116, PR China;3. National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, Zhejiang 310027, PR China;4. School of Mathematics and Physics, Xuzhou Institute of Technology, Xuzhou, Jiangsu 221000, PR China;1. Department of Mathematics, Bharathiar University, Coimbatore - 641046, Tamilnadu, India;2. Center for Intelligent Systems Research, Geelong Waurn Ponds Campus, Deakin University, Victoria, Australia;1. School of Electrical Engineering, Chungbuk National University, 52 Naesudong-ro, Cheongju 361-763, Republic of Korea;2. Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 280 Daehak-ro, Gyeongsan 712-749, Republic of Korea;3. School of Electronic Engineering, Daegu University, Gyeongsan 712-714, Republic of Korea;4. Department of Biomedical Engineering, School of Medicine, Chungbuk National University, 52 Naesudong-ro, Cheongju 361-763, Republic of Korea;1. Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of Korea;2. National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Yuquan Campus, Hangzhou, Zhejiang, 310027, PR China |
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| Abstract: | Generalized synchronization (GS) occurs when the states of one system, through a functional mapping are equal to states of another. Since for many physical systems only some state variables are observable, it seems convenient to extend the theoretical framework of synchronization to consider such situations. In this contribution, we investigate two variants of GS which appear between strictly different chaotic systems. We consider that for both the drive and response systems only one observable is available. For the case when both systems can be taken to a complete triangular form, a GS can be achieved where the functional mapping between drive and response is found directly from their Lie-algebra based transformations. Then, for systems that have dynamics associated to uncontrolled and unobservable states, called internal dynamics, where only a partial triangular form is possible via coordinate transformations, for this situation, a GS is achieved for which the coordinate transformations describe the functional mapping of only a few state variables. As such, we propose definitions for complete and partial-state GS. These particular forms of GS are illustrated with numerical simulations of well-known chaotic benchmark systems. |
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