Numerical simulations of periodic and chaotic responses in a stable duffing system |
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| Affiliation: | 1. Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran;2. School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran;3. Nano-Robotics Laboratory, Center of Excellence in Design, Robotics & Automation, School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran;1. Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile;2. Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France;1. Research Center of Advanced Intelligent Materials and Structures (AIMS), University of Michigan and Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, 800 Dongchuan Rd, Shanghai 200240, China;2. State Key Laboratory of Mechanical Systems and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China |
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| Abstract: | A stable Duffing system is examined by numerical simulations in order to obtain a better understanding of the behavior of periodic and chaotic responses to sinusoidal excitations. It is found that beside the multiplicity of responses, there is a duality for both periodic and chaotic responses. Period doubling does exist and this process may originate from different basic responses even with the same forcing frequency. The evolution of chaos is shown by a sequence of Poincaré maps. Finally a possible pattern for transition to chaos is suggested. |
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