Role of parametric resonance in the inhibition of chaotic escape from a potential well |
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| Institution: | 1. College of Geography and Environmental Science, Baoji University of Arts and Sciences, Baoji 721013, China;2. Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji 721016, China;3. College of Mechanical Engineering, Baoji University of Arts and Sciences, Baoji 721016, China;4. Shaanxi Key Laboratory of Advanced Manufacturing and Evaluation of Robot Key Components, Baoji 721016, China;1. Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran;2. Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam;3. Department of Computer Science and Electrical Engineering, Jacobs University, Bremen gGmbH, Germany;4. Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China;1. Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China;2. School of Physics and Information Technology, Shaanxi Normal University, Xian 710062, China;3. Department of Anorectal Surgert, the 1st Peoples Hospital of Yunnan Province, Kunhua Hospital Affiliated to Kunming Univesity of Science and Techhologey, Kunming 650032, China;4. Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji 721016, China |
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| Abstract: | This paper shows how a periodic parametric modulation can inhibit chaotic escape of a driven oscillator from the cubic potential well that typically models a metastable system close to a fold. Melnikov analysis shows that, depending on its amplitude, period, and initial phase, a periodic parametric modulation of the linear potential term suppresses chaotic escape when certain resonance conditions are met. In particular, it is shown that chaotic escape suppression is impossible under a period-1 parametric perturbation. The effect of nonlinear damping on the inhibition scenario is also studied. |
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