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contributor authorAlbert C. Luo
date accessioned2017-05-09T00:22:56Z
date available2017-05-09T00:22:56Z
date copyrightJuly, 2007
date issued2007
identifier issn1555-1415
identifier otherJCNDDM-25622#242_1.pdf
identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/135326
description abstractIn this paper, the global transversality and tangency in two-dimensional nonlinear dynamical systems are discussed, and the exact energy increment function (L-function) for such nonlinear dynamical systems is presented. The Melnikov function is an approximate expression of the exact energy increment. A periodically forced, damped Duffing oscillator with a separatrix is investigated as a sampled problem. The corresponding analytical conditions for the global transversality and tangency to the separatrix are derived. Numerical simulations are carried out for illustrations of the analytical conditions. From analytical and numerical results, the simple zero of the energy increment (or the Melnikov function) may not imply that chaos exists. The conditions for the global transversality and tangency to the separatrix may be independent of the Melnikov function. Therefore, the analytical criteria for chaotic motions in nonlinear dynamical systems need to be further developed. The methodology presented in this paper is applicable to nonlinear dynamical systems without any separatrix.
publisherThe American Society of Mechanical Engineers (ASME)
titleOn Global Transversality and Chaos in Two-Dimensional Nonlinear Dynamical Systems
typeJournal Paper
journal volume2
journal issue3
journal titleJournal of Computational and Nonlinear Dynamics
identifier doi10.1115/1.2727494
journal fristpage242
journal lastpage248
identifier eissn1555-1423
keywordsMotion
keywordsChaos
keywordsNonlinear dynamical systems
keywordsComputer simulation AND Flow (Dynamics)
treeJournal of Computational and Nonlinear Dynamics:;2007:;volume( 002 ):;issue: 003
contenttypeFulltext


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