Adaptive synchronization in tree-like dynamical networks |
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| Institution: | 1. Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, Ecole des Ponts ParisTech, IFSTTAR, F-77455 Marne-la-Vallée, France;2. Université Paris-Est, MAST, SDOA, IFSTTAR, F-77447 Marne-la-Vallée, France;1. School of Mathematics, Southeast University, Nanjing 210096, China;2. School of Automation and Electrical Engineering, Linyi University, Linyi 276005, Shandong, China;3. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;4. School of Information Science and Engineering, Southeast University, Nanjing 210096, China;5. Texas A&M University at Qatar, Doha 23874, Qatar;6. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China |
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| Abstract: | Synchronization in an array of coupled identical nonlinear dynamical systems have attracted increasing attention from various fields of science and engineering. In this paper, we investigate the synchronization phenomenon in tree-like dynamical networks. Based on the LaSalle invariant principle, a simple and systematic adaptive control scheme with variable coupling strength is proposed for the synchronization of tree-like dynamical networks without any knowledge of the concrete structure of isolate system. This result indicates that synchronization can be achieved for strong enough coupling if there exists a system (located at the root of the tree) which directly or indirectly influences all other systems. Furthermore, the main result is applied to several Lorenz chaotic systems coupled by a tree. And numerical simulations are also given to show the effectiveness of the proposed synchronization method. |
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