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.

引用

页码：1052 / 1094

页数：43

共 59 条

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