Quasiperiodic resonance and bifurcations of tori in the weakly nonlinear Duffing oscillator

DOI10.1016/0167-2789(92)90079-3zbMath0767.34021OpenAlexW2051653914MaRDI QIDQ1196061

Andrey B. Belogortsev

Publication date: 18 January 1993

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

Full work available at URL: https://doi.org/10.1016/0167-2789(92)90079-3

zbMATH Keywords

averagingfrequency response functionsperiod doublingquasiperiodic Duffing equationsecondary cuspsvan der Pol transformation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27)

Related Items (3)

On Global Dynamics in Duffing Equation with Quasiperiodic Perturbation ⋮ Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasi-periodic Perturbation ⋮ On Quasi-Periodic Parametric Perturbations of Hamiltonian Systems

Cites Work

• Unnamed Item
• Second-order averaging and chaos in quasiperiodically forced weakly nonlinear oscillators
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Universality and self-similarity in the bifurcations of circle maps
• The variational approach to the theory of subharmonic bifurcations
• Numerical simulations of periodic and chaotic responses in a stable Duffing system
• Secondary resonances and approximate models of routes to chaotic motion in non-linear oscillators
• On necessary and sufficient conditions for chaos to occur in Duffing's equation: an Heuristic approach
• On the transition from regular to chaotic behaviour in the Duffing oscillator
• Chaotic motion of a weakly nonlinear, modulated oscillator

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