Remarks on transitions order-chaos induced by the shape of the periodic excitation in a parametric pendulum.

DOI10.1016/0960-0779(95)00066-6zbMath1080.70535OpenAlexW2067131137MaRDI QIDQ815530

Miguel A. F. Sanjuán

Publication date: 17 February 2006

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0960-0779(95)00066-6

zbMATH Keywords

Melnikov analysisJacobi elliptic functionhomoclinic bifurcations

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Dynamical systems in classical and celestial mechanics (37N05)

Related Items (8)

ANALYTICAL ESTIMATES OF THE EFFECT OF NONLINEAR DAMPING IN SOME NONLINEAR OSCILLATORS ⋮ Optimal Control of Homoclinic Bifurcation: Theoretical Treatment and Practical Reduction of Safe Basin Erosion in the Helmholtz Oscillator ⋮ On the occurrence of chaos in a parametrically driven extended Rayleigh oscillator with three-well potential ⋮ Steady state, oscillations and chaotic behavior of a gas inside a cylinder with a mobile piston controlled by PI and nonlinear control ⋮ A generalized perturbed pendulum. ⋮ Effect of nonlinear dissipation on the basin boundaries of a driven two-well Rayleigh-Duffing oscillator ⋮ A pendulum with an elliptic-type parametric excitation: stability charts for a damped and undamped system ⋮ Subharmonic bifurcations in a pendulum parametrically excited by a non-harmonic perturbation

Cites Work

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• Subharmonic and homoclinic bifurcations in a parametrically forced pendulum
• Elliptic functions and applications

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