Fractal basins and chaotic bifurcations prior to escape from a potential well |
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| Affiliation: | 1. College of Civil Engineering and Mechanics, Central South University of Forestry and Technology, Changsha, Hunan 410004, PR China;2. Hunan Province Key Laboratory of Engineering Rheology, Central South University of Forestry and Technology, Changsha, Hunan 410004, PR China;3. School of Civil Engineering and Architecture, Changsha University of Science and Technology, Changsha 410004, PR China;1. Department of Electrical Engineering, Islamic Azad University, South Tehran Branch, Tehran, P.O. Box 11365-4435, Iran;2. Department of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran, P.O. Box 14588-89694, Iran;1. Department of Mathematics, University of Delhi, Delhi, India;2. Department of Mathematics, Jamia Millia Islamia, Delhi, India;3. Department of Mathematics, Kirorimal College, University of Delhi, Delhi, India |
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| Abstract: | The escape of a periodically driven damped oscillator from a potential well is intimately associated with homoclinic tangles, fractal basins, and a variety of chaotic bifurcations. A bifurcation diagram, including an analytical Melnikov solution is presented for a canonical asymmetric cubic potential, and comparisons are made with recent results for the Holmes two-well oscillator. |
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