Survey of regular and chaotic phenomena in the forced Duffing oscillator

DOI10.1016/0960-0779(91)90032-5zbMath0748.34022OpenAlexW2065382523MaRDI QIDQ1185418

Yoshisuke Ueda

Publication date: 28 June 1992

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0960-0779(91)90032-5

zbMATH Keywords

oscillatorglobal bifurcationsdiscrete dynamical systemscoexisting attractorschaotic motionsfractal basin boundariesanalog and digital simulationgeometric theory of dynamical systemsnonlinear differential equations of the second order

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Bifurcations and instability for nonlinear problems in mechanics (70K50) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Attractors of solutions to ordinary differential equations (34D45) Dynamical systems and ergodic theory (37-XX)

Related Items (20)

BIFURCATION STRUCTURES GENERATED BY THE NONAUTONOMOUS DUFFING EQUATION ⋮ Lyapunov exponents for a Duffing oscillator ⋮ Quasilinear systems with unpredictable relay perturbations ⋮ Solutions of a class of Duffing oscillators with variable coefficients ⋮ Antiperiodic oscillations in a forced Duffing oscillator ⋮ Controlling chaotic oscillators without feedback ⋮ Chaotic dynamics of a simple oscillator - A pictorial introduction ⋮ CATASTROPHE THEORETIC CLASSIFICATION OF NONLINEAR OSCILLATORS ⋮ Prediction of bifurcations and chaos for an asymmetric elastic oscillator ⋮ Controlling Nonlinear Dynamics in a Two-Well Impact System. ⋮ Controlling Nonlinear Dynamics in a Two-Well Impact System. ⋮ A secure communication scheme based on chaotic Duffing oscillators and frequency estimation for the transmission of binary-coded messages ⋮ NEW PHENOMENA IN THE NEIGHBORHOOD OF THE CODIMENSION-TWO BIFURCATION IN THE TWIN-WELL DUFFING OSCILLATOR ⋮ TANGLED SEPARATRICES ON TWO DEGREES OF FREEDOM SWING EQUATION SYSTEM ⋮ BEHAVIOR OF HARMONICS GENERATED BY A DUFFING TYPE EQUATION WITH A NONLINEAR DAMPING: PART I ⋮ Chaos from two modified oscillator configurations using a current feedback op amp ⋮ HIGH-DIMENSIONAL CHAOS IN DISSIPATIVE AND DRIVEN DYNAMICAL SYSTEMS ⋮ Bifurcations phenomena in a nonlinear oscillator: Approximate analytical studies versus computer simulation results ⋮ Symbolic dynamics of the Lorenz equations. ⋮ Non-linearity, bifurcation and chaos in the finite dynamics of different cable models.

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Strange attractors
• Basin boundary metamorphoses: Changes in accessible boundary orbits
• Transformation theory as applied to the solutions of non-linear differential equations of the second order
• Note concerning our paper On the nature of turbulence. Commun. math. Phys. 20, 167-192 (1971)
• The number of subharmonic solutions of non-linear differential equations of the second order
• Catastrophes with indeterminate outcome
• Bifurcation and catastrophe theory
• Crises, sudden changes in chaotic attractors, and transient chaos
• An Improved Closing Lemma and a General Density Theorem
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• On The Existence of Periodic Solutions For Second Order Differential Equations with a Forcing Term
• On a Non‐linear Differential Equation of the Second Order
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Survey of regular and chaotic phenomena in the forced Duffing oscillator