Fractal basins and chaotic bifurcations prior to escape from a potential well

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 potentia...

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Bibliographic Details
Published inPhysics letters. A Vol. 121; no. 3; pp. 116 - 120
Main Authors Thompson, J.M.T., Bishop, S.R., Leung, L.M.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 13.04.1987
Elsevier Science
Subjects
Applied sciences
Exact sciences and technology
Other techniques and industries
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Summary: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.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(87)90403-8