Chaotic Dynamics of Quasi-Periodically Forced Oscillators Detected by Melnikov’s Method

DOI10.1137/0523069zbMath0813.34047OpenAlexW1970503307MaRDI QIDQ4020412

Kazuyuki Yagasaki

Publication date: 16 January 1993

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0523069

zbMATH Keywords

chaoshomoclinic orbitsplanar Hamiltonian systemsquasiperiodic perturbationsquasiperiodic systemsMel'nikov's methodgeneralized Bernoulli shift

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Bifurcations and instability for nonlinear problems in mechanics (70K50) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Chaotic motions near homoclinic manifolds and resonant tori in quasiperiodic perturbations of planar Hamiltonian systems ⋮ Melnikov processes and chaos in randomly perturbed dynamical systems ⋮ Homoclinic bifurcation sets of driven nonlinear oscillators ⋮ Chaotic responses of a deformable system under parametric and external excitations. ⋮ MELNIKOV'S METHOD AND STICK–SLIP CHAOTIC OSCILLATIONS IN VERY WEAKLY FORCED MECHANICAL SYSTEMS ⋮ THE SUBHARMONIC MELNIKOV THEORY FOR DAMPED AND DRIVEN OSCILLATORS REVISITED ⋮ Horseshoe-shaped maps in chaotic dynamics of long Josephson junction driven by biharmonic signals

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