Effect of bounded noise on the chaotic motion of a Duffing-Van der Pol oscillator in a \(\phi^{6}\) potential

DOI10.1016/J.CHAOS.2005.04.048zbMath1083.37062OpenAlexW2091657382MaRDI QIDQ813568

Zhongkui Sun, Wei Xu, Xiaoli Yang

Publication date: 13 February 2006

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2005.04.048

zbMATH Keywords

Lyapunov exponentsPoincaré mapschaotic behaviornumerical simulationsbasins of attractionfractalitybifurcation surfaceshomoclinic or heteroclinic bifurcationMelnikov theorem

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Random vibrations in mechanics of particles and systems (70L05) Dynamical systems in classical and celestial mechanics (37N05) Attractors of solutions to ordinary differential equations (34D45)

Related Items (10)

Modelling of the dynamics of Euler's beam by \(\phi^6\) potential ⋮ Stochastic response of a \(\phi^6\) oscillator subjected to combined harmonic and Poisson white noise excitations ⋮ Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillator ⋮ Chaotic response of a quarter car model forced by a road profile with a stochastic component ⋮ STOCHASTIC BIFURCATION OF AN ASYMMETRIC SINGLE-WELL POTENTIAL DUFFING OSCILLATOR UNDER BOUNDED NOISE EXCITATION ⋮ BACKSTEPPING CONTROL AND SYNCHRONIZATION OF PARAMETRICALLY AND EXTERNALLY EXCITED Φ⁶ VAN DER POL OSCILLATORS WITH APPLICATION TO SECURE COMMUNICATIONS ⋮ Synchronization via active control of parametrically and externally excited Φ⁶ Van der Pol and Duffing oscillators and application to secure communications ⋮ Fuzzy Responses and Bifurcations of a Forced Duffing Oscillator with a Triple-Well Potential ⋮ THE 2-D SEXTIC HAMILTONIAN OSCILLATOR ⋮ Chaos and Chaos Control of the Frenkel–Kontorova Model with Dichotomous Noise

Cites Work

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• Determining Lyapunov exponents from a time series
• Lyapunov exponent and chaos of Duffing's equation perturbed by white noise
• Bifurcation of periodic motions in two weakly coupled van der Pol oscillators
• Global bifurcations and chaos. Analytical methods
• Prediction of horseshoe chaos in BVP and DVP oscillators
• Noise-induced chaos and phase space flux
• Resonant oscillation and homoclinic bifurcation in a \(\Phi^{6}\)-van der Pol oscillator
• Effect of bounded noise on chaotic motion of a triple-well potential system
• Strange attractors and chaos control in a Duffing–Van der Pol oscillator with two external periodic forces
• Criteria for chaos of a three-well potential oscillator with homoclinic and heteroclinic orbits
• A nonlinear oscillator with a strange attractor
• Analysis of a Nonlinear System Exhibiting Chaotic, Noisy Chaotic, and Random Behaviors

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