Evidence for homoclinic orbits as a precursor to chaos in a magnetic pendulum

DOI10.1016/0167-2789(87)90086-8zbMath0607.70027OpenAlexW1990300634MaRDI QIDQ1085646

Francis C. Moon, Philip J. Holmes, Joseph Cusumano

Publication date: 1987

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(87)90086-8

zbMATH Keywords

Numerical simulationsforced pendulumhomoclinic orbitsPoincaré mapphase space flowstrange attractorexistence of homoclinic orbitschaotic oscillationsfractal naturemagnet rotormethod of Melnikovtime- varying magnetic fieldstraveling wave force field

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (6)

Chaotic dynamics of a whirling pendulum ⋮ Alternating current-driven graphene superlattices: Kinks, dissipative solitons, dynamic chaotization ⋮ Chaos in a magnetic pendulum subjected to tilted excitation and parametric damping ⋮ Dynamics of a DC Motor-Driving Arm with a Circular Periodic Potential and DC/AC Voltage Input ⋮ Experimental measurement of chaotic attractors in solid mechanics^a) ⋮ Global optimal control and system-dependent solutions in the hardening Helmholtz--Duffing oscillator

Cites Work

• Unnamed Item
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Subharmonic and homoclinic bifurcations in a parametrically forced pendulum
• Fractal basin boundaries
• Josephson-junction circuit analysis via integral manifolds-Part II
• Josephson's junction, annulus maps, Birkhoff attractors, horseshoes and rotation sets
• A nonlinear oscillator with a strange attractor

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