COMPUTER-ASSISTED PROOF OF SHEAR-INDUCED CHAOS IN STOCHASTICALLY PERTURBED HOPF SYSTEMS

被引：5
作者：
Breden, Maxime [1 ]
Engel, Maximilian [2 ]
机构：
[1] Ecole Polytech, CMAP, Palaiseau, France
[2] Free Univ Berlin, Dept Math & Comp Sci, Berlin, Germany
来源：
ANNALS OF APPLIED PROBABILITY | 2023年 / 33卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
Homotopy method; Kolmogorov operators; Lyapunov exponents; quasi-ergodic dis-tribution; NUMERICAL VERIFICATION; EXISTENCE;
D O I：
10.1214/22-AAP1841
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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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页码：1052 / 1094
页数：43
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