Homoclinic tangles, phase locking, and chaos in a two-frequency perturbation of Duffing's equation

DOI10.1007/s003329900066zbMath0939.34039OpenAlexW2053133372MaRDI QIDQ1277234

Kazuyuki Yagasaki

Publication date: 28 June 2000

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s003329900066

zbMATH Keywords

chaosBernoulli shiftMelnikov methodphase lockinghomoclinicmulti-frequency perturbation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (8)

Chaotic motions near homoclinic manifolds and resonant tori in quasiperiodic perturbations of planar Hamiltonian systems ⋮ Unnamed Item ⋮ Bifurcations and Chaos in the Duffing Equation with Parametric Excitation and Single External Forcing ⋮ Dynamics of driven coupled oscillators with shape deformable potential. ⋮ Homotopy analysis method for approximations of Duffing oscillator with dual frequency excitations ⋮ Bursters and quasi-periodic solutions of a self-excited quasi-periodic Mathieu oscillator ⋮ Chaos in the softening Duffing system under multi-frequency periodic forces ⋮ Complex dynamics in Duffing-Van der Pol equation

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