Bifurcation analysis of a stochastically driven limit cycle

DOI10.1007/s00220-019-03298-7zbMath1414.37027arXiv1606.01137OpenAlexW3101432825WikidataQ128464391 ScholiaQ128464391MaRDI QIDQ1729879

Maximilian Engel, Jeroen S. W. Lamb, Martin Rasmussen

Publication date: 28 February 2019

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.01137

zbMATH Keywords

bifurcationLyapunov exponentsrandom strange attractorsstochastically driven limit cycle

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Generation, random and stochastic difference and differential equations (37H10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (11)

A general view on double limits in differential equations ⋮ Noise dependent synchronization of a degenerate SDE ⋮ Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems ⋮ Positive Lyapunov exponent in the Hopf normal form with additive noise ⋮ Noise and dissipation on coadjoint orbits ⋮ A random dynamical systems perspective on isochronicity for stochastic oscillations ⋮ Random switching near bifurcations ⋮ A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations ⋮ Conditioned Lyapunov exponents for random dynamical systems ⋮ Ruelle-Pollicott resonances of stochastic systems in reduced state space. Part II: Stochastic Hopf bifurcation ⋮ Stochastic n-point D-bifurcations of stochastic Lévy flows and their complexity on finite spaces

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• Shear-induced chaos
• Chaotic phenomena in three settings: large, noisy and out of equilibrium
• Markov measures for random dynamical systems
• Hopf bifurcation with additive noise

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