Periodic and chaotic synchronizations of two distinct dynamical systems under sinusoidal constraints |
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| Authors: | Fuhong Min Albert CJ Luo |
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| Institution: | 1. School of Electrical Engineering and Automation, Nanjing Normal University, Nanjing, Jiangsu 210042, PR China;2. Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA;1. Departamento de Físico Matemáticas, Instituto de Investigación en Comunicación Óptica, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, Centro, 78000 S.L.P., Mexico;2. Academia de Matemáticas, Universidad Politécnica de San Luis Potosí, Urbano Villalón 500, 78369 S.L.P., Mexico;3. División de Matemáticas Aplicadas, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la Presa San José 2055, Lomas 4 secc. 78216 S.L.P., Mexico;4. Centro de Investigaciones en Optica, Loma del Bosque 115, Lomas del Campestre, 37150 Leon, Gto., Mexico;1. School of Naval Architecture, Ocean and Civil Engineering (State Key Laboratory of Ocean Engineering), Shanghai Jiao Tong University, Shanghai 200240, PR China;2. School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore;1. Department of Mechanical Engineering, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iran;2. Department of Mechanical Engineering, University of Guilan, P.O. Box 41635-3756, Rasht, Iran;1. Department of Aerospace Engineering, University of Illinois, Urbana, IL, United States;2. Department of Electrical Engineering, University of Illinois, Urbana, IL, United States |
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| Abstract: | In this paper, periodic and chaotic synchronizations between two distinct dynamical systems under specific constraints are investigated from the theory of discontinuous dynamical systems. The analytical conditions for the sinusoidal synchronization of the pendulum and Duffing oscillator were obtained, and the invariant domain of sinusoidal synchronization is achieved. From analytical conditions, the control parameter map is developed. Numerical illustrations for partial and full sinusoidal synchronizations of chaotic and periodic motions of the controlled pendulum with the Duffing oscillator are carried out. This paper presents how to apply the theory of discontinuous dynamical systems to dynamical system synchronization with specific constraints. The function synchronization of two distinct dynamical systems with specific constraints should be identified only by G-functions. The significance of function synchronization of distinct dynamical systems is to make the synchronicity behaviors hidden, which is very useful for telecommunication synchronization and network security. |
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