The bifurcation to homoclinic tori in the quasiperiodically forced Duffing oscillator

DOI10.1016/0167-2789(89)90232-7zbMath0673.58031OpenAlexW2038420970MaRDI QIDQ1120875

Kayo Ide, Stephen Wiggins

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0167-2789(89)90232-7

zbMATH Keywords

chaotic dynamicsbifurcation to homoclinic toriquasiperiodically forced Duffing oscillator

Mathematics Subject Classification ID

Local and nonlocal bifurcation theory for dynamical systems (37G99) Dynamical systems with hyperbolic behavior (37D99)

Related Items (12)

Chaotic motions near homoclinic manifolds and resonant tori in quasiperiodic perturbations of planar Hamiltonian systems ⋮ Invariant manifold templates for chaotic advection ⋮ Periodically forced double homoclinic loops to a dissipative saddle ⋮ Optimal Control of Homoclinic Bifurcation: Theoretical Treatment and Practical Reduction of Safe Basin Erosion in the Helmholtz Oscillator ⋮ Homoclinic bifurcation sets of driven nonlinear oscillators ⋮ Dynamics of homoclinic tangles in periodically perturbed second-order equations ⋮ Frictional oscillations under the action of almost periodic excitation ⋮ Homoclinic bifurcation in a quasiperiodically excited impact inverted pendulum ⋮ Chaos in the softening Duffing system under multi-frequency periodic forces ⋮ Chaos in mechanical systems -- a review ⋮ Silnikov's orbit in coupled Duffing's systems ⋮ Quasi-periodic solutions and sub-harmonic bifurcation of Duffing's equations with quasi-periodic perturbation

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Global bifurcations and chaos. Analytical methods
• Chaotic solutions of systems with almost periodic forcing
• Melnikov Transforms, Bernoulli Bundles, and Almost Periodic Perturbations
• Crises, sudden changes in chaotic attractors, and transient chaos
• On the Theory of Quasiperiodic Motions
• Invariant manifolds
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