Homoclinic bifurcation and chaos in simple pendulum under bounded noise excitation

DOI10.1016/j.chaos.2003.08.010zbMath1054.70017OpenAlexW2054120189MaRDI QIDQ1878083

Yanyan Li

Publication date: 19 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2003.08.010

zbMATH Keywords

Poincaré mapsLyapunov exponentrandom Melnikov process

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Random vibrations in mechanics of particles and systems (70L05) Dynamical systems in classical and celestial mechanics (37N05) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44)

Related Items (11)

COMPLEX DYNAMICS IN PENDULUM EQUATION WITH PARAMETRIC AND EXTERNAL EXCITATIONS I ⋮ Chaos control in a pendulum system with excitations ⋮ Melnikov analysis of chaos in a simple SIR model with periodically or stochastically modulated nonlinear incidence rate ⋮ COMPLEX DYNAMICS IN A PENDULUM EQUATION WITH A PHASE SHIFT ⋮ Codimension 3 nontwisted double homoclinic loops bifurcations with resonant eigenvalues ⋮ Complex dynamics in physical pendulum equation with suspension axis vibrations ⋮ Codimension 2 bifurcations of double homoclinic loops ⋮ Stability of Ships with Water on Deck in Random Beam Waves ⋮ Chaos control in a special pendulum system for ultra-subharmonic resonance ⋮ STOCHASTIC BIFURCATION OF AN ASYMMETRIC SINGLE-WELL POTENTIAL DUFFING OSCILLATOR UNDER BOUNDED NOISE EXCITATION ⋮ Classification of homoclinic tangencies for periodically perturbed systems

Cites Work

• Determining Lyapunov exponents from a time series
• Global bifurcations and chaos. Analytical methods
• Noise-induced chaos and phase space flux
• Effect of bounded noise on chaotic motion of Duffing oscillator under parametric excitation
• Analysis of a Nonlinear System Exhibiting Chaotic, Noisy Chaotic, and Random Behaviors
• Invariant measure of a driven nonlinear oscillator with external noise
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