The dynamics of stochastic and resonant layers in a periodically driven pendulum

DOI10.1016/S0960-0779(99)00162-9zbMath0962.70024MaRDI QIDQ1581722

Albert C. J. Luo, Ray P. S. Han

Publication date: 8 October 2000

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

zbMATH Keywords

homoclinic orbitPoincaré mapping sectionsstochastic layersperiodically driven pendulumresonant layersresonant separatrixsub-resonancewhisker map

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55)

Related Items (9)

Stochastic dynamics of electric dipole in external electric fields: a perturbed nonlinear pendulum approach ⋮ Deterministic models for simulating electrocardiographic signals ⋮ Periodic and chaotic synchronizations of two distinct dynamical systems under sinusoidal constraints ⋮ CHAOTIC BEHAVIOR AND SUBHARMONIC BIFURCATIONS FOR A ROTATING PENDULUM EQUATION ⋮ Synchronization of a periodically forced Duffing oscillator with a periodically excited pendulum ⋮ Chaotic motions in the resonant separatrix band of a parametrically excited pendulum ⋮ Resonance and chaotic trajectories in magnetic field reversed configuration ⋮ Sinusoidal synchronization of a Duffing oscillator with a chaotic pendulum ⋮ Phase Shadows: An Enhanced Representation of Nonlinear Dynamic Systems

Cites Work

• Transport rates of a class of two-dimensional maps and flows
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Regular and chaotic dynamics.
• Hamiltonian algorithms for Hamiltonian systems and a comparative numerical study
• Resonant-separatrix webs in stochastic layers of the twin-well Duffing oscillator
• Analysis of the separatrix map in Hamiltonian systems
• The accuracy of symplectic integrators
• Secondary homoclinic bifurcation theorems
• Homoclinic tangles-classification and applications

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