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Modulation of synchronization dynamics in a network of self-sustained systems
Institution:1. Monell Chemical Senses Center, 3500 Market Street, Philadelphia, PA 19104, USA;2. Institut de Mathématiques et de Sciences Physiques, B.P. 613, Porto-Novo, Benin;3. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain;1. School of Mathematical Sciences, Shandong Normal University, Ji’nan 250014, PR China;2. Research Center on Logistics optimization and Prediction of Engineering Technology, Ji’nan, Shandong 250014, PR China;1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, PR China;2. School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 610054, PR China;3. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, PR China;4. School of Mathematics and Computer Science, Yunnan University of Nationalities, Kunming 650031, PR China;1. Departamento de Matemáticas, Centro de Investigación de Física Teórica y Matemática FIMAT, University of Huelva, 21071 Huelva, Spain;2. Departamento de Matemática Aplicada II, E.S. Ingenieros, University of Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain;1. Macedonian Academy of Sciences and Arts, Skopje, Macedonia;2. BioCircuits Institute, University of California, San Diego, La Jolla, CA 92093-0402, USA;1. Universidade Nove de Julho, Departamento de Informática, Rua Guaranésia, n. 425, CEP 02112-000, São Paulo, SP, Brazil;2. Universidade Presbiteriana Mackenzie, Escola de Engenharia, Pós-Graduação em Engenharia Elétrica, Rua da Consolação, n. 896, CEP 01302-907, São Paulo, SP, Brazil;3. Universidade de São Paulo, Escola Politécnica, Departamento de Engenharia de Telecomunicações e Controle, Av. Prof. Luciano Gualberto, travessa 3, n. 380, CEP 05508-900, São Paulo, SP, Brazil
Abstract:This paper addresses the combined modulatory effects of non-nearest neighbor oscillators and local injection on synchronized states dynamics with their corresponding stability boundaries in a network of self-sustained systems. The Whittaker method and Floquet theory are used to predict analytically the stability of these states for identical and non-identical coupling parameters. Charts revealing the modulation of synchronized states and their stability boundaries at the second order of interaction in the cases of identical and non-identical coupling parameters are constructed with and without an external signal locally injected in the network. Numerical simulations validate and complement the results of analytical surveys. The limits of the stability regions are numerically explored when a small amount of Gaussian white noise is also injected in the network.
Keywords:Phase synchronization  Self-sustained systems  Local injection  Noise
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