Adaptive coupled synchronization among multi-Lorenz systems family |
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| Institution: | 1. School of Automation and Electrical Engineering & Key Laboratory of Complex systems and Intelligent Computing in Universities of Shandong, Shandong, Linyi University, Linyi 276005, China;2. College of Engineering, Qufu Normal University, Rizhao 273165, China;3. School of Mathematics, Southeast University, Nanjing 210096, China;4. Department of Electrical Engineering, Yeungnam University, Kyongsan 38541, Republic of Korea;5. School of Mathematical Sciences, Shandong Normal University, Ji’nan, 250014 Shandong, China |
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| Abstract: | In this paper, the adaptive synchronization method of coupled system is proposed for multi-Lorenz systems family. This method can avoid estimating the value of coupling coefficient. Strict theoretical proofs are given. And we derived a sufficient condition of synchronization for a general unidirectional coupling ring network with N identical Lorenz systems. The network is coupled through the first state variable of each equation. In fact, the whole unidirectional coupling network will synchronize by adding only one adaptive feedback gain equation. Numerical simulations show the effectiveness of the methods. |
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