Deterministic and stochastic Duffing-van der Pol oscillators are non-explosive

DOI10.1007/BF00915273zbMath0876.70018OpenAlexW2146641136MaRDI QIDQ2365363

Klaus Reiner Schenk-Hoppé

Publication date: 2 December 1997

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00915273

zbMATH Keywords

white noisestate spacebackward solutionsbifurcation parametersforward solutioncompleteness of stochastic differential systemsintensity parameters

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Random vibrations in mechanics of particles and systems (70L05) Ordinary differential equations and systems with randomness (34F05)

Related Items (9)

A new model for realistic random perturbations of stochastic oscillators ⋮ Hopf bifurcation with additive noise ⋮ On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients ⋮ An analysis of the effect of noise in a heterogeneous agent financial market model ⋮ Mean-square convergence analysis of the semi-implicit scheme for stochastic differential equations driven by the Wiener processes ⋮ Random attractions and bifurcation for the classical Rayleigh-Van der Pol equations with small noise ⋮ A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, and perturbations ⋮ The stochastic FitzHugh-Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model ⋮ The fully implicit stochastic-\(\alpha \) method for stiff stochastic differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Explosion time of second-order Ito processes
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Phase portraits and bifurcations of the non-linear oscillator: \(x+(\alpha+\gamma x^ 2)x'+\beta x+\delta x^ 3=0\)
• Temps d'explosion d'équations différentielles stochastiques du type Doléans-Dade. (Explosion times for solutions of Doléans-Dade stochastic differential equations)
• On the gap between deterministic and stochastic ordinary differential equations
• Strong \(p\)-completeness of stochastic differential equations and the existence of smooth flows on noncompact manifolds
• Stochastic non-linear oscillators
• Hopf Bifurcation in the Presence of Both Parametric and External Stochastic Excitations
• Stochastic bifurcation

This page was built for publication: Deterministic and stochastic Duffing-van der Pol oscillators are non-explosive