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Homoclinic transition to chaos in the Ueda oscillator with external forcing

Grzegorz Litak·Arkadiusz Syta·Marek Borowiec
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Abstract

We examine the Melnikov criterion for transition to chaos in case of a single degree of freedom nonlinear oscillator with the Ueda well potential and an external periodic excitation term. Using effective Hamiltonian we have examined homoclinic orbits and cross-sections of stable and unstable manifolds which gave the condition of transition to chaos through a homoclinic bifurcation.

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Grzegorz Litak, Arkadiusz Syta, Marek Borowiec. 2006-10-09. Homoclinic transition to chaos in the Ueda oscillator with external forcing. https://arxiv.org/abs/nlin/0610018

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