On the stationary distribution of self-sustained oscillators around bifurcation points.

DOI10.1007/BF01019146zbMath1084.37519OpenAlexW1632394513MaRDI QIDQ1963574

Tamás Tél

Publication date: 2 February 2000

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01019146

zbMATH Keywords

Hopf bifurcationvan der Pol oscillatorStationary distributionweak noise expansion

Mathematics Subject Classification ID

Chemistry (92E99) Random vibrations in mechanics of particles and systems (70L05) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31) Bifurcation theory for random and stochastic dynamical systems (37H20)

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Semi-analytical expression of stochastic closed curve attractors in nonlinear dynamical systems under weak noise ⋮ Stationary distribution of stochastic Markov jump coupled systems based on graph theory ⋮ Stochastic analysis of a noisy oscillator

Cites Work

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• The Fokker-Planck equation. Methods of solution and applications
• Asymptotic properties of coupled nonlinear Langevin equations in the limit of weak noise. II: Transition to a limit cycle
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Handbook of stochastic methods for physics, chemistry and the natural sciences
• Stochastic analysis of symmetry-breaking bifurcations: Master equation approach
• On the weak-noise limit of Fokker-Planck models
• On the theory of optimal control. Sufficient coordinates
• Diffusion Across Characteristic Boundaries
• Large fluctuations for a nonlinear heat equation with noise
• ON SMALL RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS
• Persistence of Dynamical Systems under Random Perturbations
• ON SMALL RANDOM PERTURBATIONS OF SOME SMOOTH DYNAMICAL SYSTEMS
• Influence of Noise on Duffing‐Van der Pol Oscillators
• A Ray Method for the Asymptotic Solution of the Diffusion Equation