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Journal Articles The Annals of Applied Probability Year : 2023

Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems

Abstract

We confirm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. The method of showing the main chaotic property, a positive Lyapunov exponent, is a computer-assisted proof. Using the recently developed theory of conditioned Lyapunov exponents on bounded domains and the modified Furstenberg-Khasminskii formula, the problem boils down to the rigorous computation of eigenfunctions of the Kolmogorov operators describing distributions of the underlying stochastic process.
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Dates and versions

hal-03168199 , version 1 (12-03-2021)
hal-03168199 , version 2 (22-11-2023)

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Cite

Maxime Breden, Maximilian Engel. Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems. The Annals of Applied Probability, 2023, 33 (2), pp.1252-1294. ⟨10.1214/22-AAP1841⟩. ⟨hal-03168199v2⟩
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