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Homoclinic and heteroclinic chaos in a triple-well oscillator

✍ Scribed by R. Chacón; J. Dı́az Bejarano

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
414 KB
Volume
186
Category
Article
ISSN
0022-460X

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✦ Synopsis

Holmes-Melnikov criteria for chaotic vibrations of a non-linear oscillator having three stable and two unstable equilibrium positions are obtained in analytic form. The chaotic threshold for homoclinic and heteroclinic bifurcations is studied as a function of two parameters: the frequency v of the driving term, and the ratio between the stable and unstable equilibrium positions x0. It is shown that the limits x0:0, 1 connect with two related Duffing and anti-Duffing type oscillators. For a set of parameter values in the region of particular interest, excellent agreement is obtained between the theoretical predictions and numerical calculations. Additionally, as x0:1, ever-longer-lasting intermittent transient motion is observed at vmax-the most chaotic frequency for homoclinic bifurcation.

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✍ Wanda Szemplińska-Stupnicka 📂 Article 📅 1992 🏛 Springer Netherlands 🌐 English ⚖ 970 KB

The paper is devoted to the study of common features in regular and strange behavior of the three classic dissipative softening type driven oscillators: (a) twin-well potential system, (b) single-well potential unsymmetric system and (c) single-well potential symmetric system. Computer simulations