RESONANT-OVERLAP PHENOMENA IN STOCHASTIC LAYERS OF NON-LINEAR HAMILTONIAN SYSTEMS WITH PERIODICAL EXCITATIONS
✍ Scribed by A.C.J. LUO
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 317 KB
- Volume
- 240
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
An accurate standard-map approach, instead of the approximate standard-map approach, is developed for the analytical prediction of the onset of a new resonant overlap forming a new resonant-separatrix web in the stochastic layer. This accurate approach applies to the twin-well Du$ng oscillator for illustration of the resonant overlap phenomena in stochastic layers. The excitation strengths are obtained analytically for the onset of the speci"ed resonant-separatrix webs in the stochastic layer. This accurate approach gives a very good prediction compared to numerical results for the lower order resonant overlap. When excitation strength is very weak, the accurate and approximate standard-map methods are in good agreement, and the accurate one is applicable to non-linear systems with strong excitations. However, the further improvement should be completed for a more accurate, analytical prediction of the onset of a new resonant overlap in stochastic layers of non-linear Hamiltonian systems with periodical excitations.