Homoclinic transition to chaos in the Ueda oscillator with external forcing

Details Homoclinic transition to chaos in the Ueda oscillator with external forcing Homoclinic transition to chaos in the Ueda oscillator with external forcing

2006-10-09

arxiv.org/abs/nlin/0610018v1

Nonlinear Sciences

Chaotic Dynamics

16 pages, 9 figures

Scientific paper

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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