Synchronization analysis of coupled Lienard-type oscillators by averaging |
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| Authors: | S. Emre Tuna |
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| Affiliation: | 1. Faculty of Mathematics, Universität Duisburg–Essen, 45117 Essen, Germany;2. Institute for Mathematics and Scientific Computing, Karl-Franzens-Universität Graz, Heinrichstr. 36, 8010 Graz, Austria;3. Computational and Applied Mathematics Group, Computer Science and Mathematics Division, Oak Ridge National Laboratory, P.O. Box 2008 Oak Ridge, TN 37831, USA;1. Faculty of Biosciences and Medical Engineering, Universiti Teknologi Malaysia, Johor bahru, 8130 Skudai, Malaysia;2. Dept. of Biomedical Eng, Faculty of Engineering, Future University, 10553 Khartoum, Sudan;1. College of Mechanical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China;2. Science and Technology on Nano/Micro Fabrication Technology, Research Institute of Micro/Nano Science and Technology, Shanghai Jiao Tong University, Shanghai 200240, China |
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| Abstract: | Sufficient conditions for the synchronization of coupled Lienard-type oscillators are investigated via averaging technique. The coupling considered here is fixed, nonsymmetric, and nonlinear. Under the assumption that the interconnection topology defines a connected graph, it is shown that the solutions of oscillators converge arbitrarily close to each other, starting from initial conditions arbitrarily far apart, provided that the frequency of oscillations is large enough and the initial phases of oscillators all lie in an open semicircle. It is also shown that the nearly-synchronized oscillations always take place around some fixed magnitude independent of the initial conditions and the coupling functions. |
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