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A Shooting Approach to Layers and Chaos in a Forced Duffing Equation

✍ Scribed by Shangbing Ai; Stuart P Hastings

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 560 KB
Volume: 185
Category: Article
ISSN: 0022-0396
DOI: 10.1006/jdeq.2002.4166

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✦ Synopsis

We study equilibrium solutions for the problem

Using a shooting method we find solutions for all nonzero e: For small e we add to the solutions found by previous authors, especially Angenent, Mallet-Paret and Peletier, and Hale and Sakamoto, and also give new elementary ode proofs of their results. Among the new results is the existence of internal layer-type solutions. Considering the ode satisfied by equilibria, but on an infinite interval, we obtain chaos results for l5l 0 ¼ 3 2 2=3 and 05e4 1 4 : We also consider the problem of bifurcation of solutions as l increases.

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