Noise induced order for skew-products over a non-uniformly expanding base

Noise-induced order is the phenomenon by which the chaotic regime of a deterministic system is destroyed in the presence of noise. In this manuscript, we establish noise-induced order for a natural class of systems of dimension ≥ 2 consisting of a fiber-contracting skew product a over nonuniformlyexpanding 1-dimensional system.

[1]  Michał Misiurewicz,et al.  Absolutely continuous measures for certain maps of an interval , 1981 .

[2]  Gregoire Nicolis,et al.  Stochastic resonance , 2007, Scholarpedia.

[3]  A note on the strong Feller property of diffusion processes , 2020, 2001.09919.

[4]  Warwick Tucker,et al.  Validated Numerics: A Short Introduction to Rigorous Computations , 2011 .

[5]  José F. Alves,et al.  Statistical instability for contracting Lorenz flows , 2019, Nonlinearity.

[6]  P. Landa.  Mechanism of stochastic resonance , 2004 .

[7]  W. Tucker.  The Lorenz attractor exists , 1999 .

[8]  V. Baladi,et al.  Strong stochastic stability and rate of mixing for unimodal maps , 1996 .

[9]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[10]  Stefano Galatolo,et al.  Existence of noise induced order, a computer aided proof , 2017, Nonlinearity.

[11]  Alvaro Rovella,et al.  The dynamics of perturbations of the contracting Lorenz attractor , 1993 .

[12]  Jianbo Gao,et al.  NOISE-INDUCED CHAOS , 1999 .

[13]  Stochastic Stability¶for Contracting Lorenz Maps and Flows , 2000 .

[14]  Yun Yang,et al.  Positive Lyapunov exponent for random perturbations of predominantly expanding multimodal circle maps , 2018, Annales de l'Institut Henri Poincaré C, Analyse non linéaire.

[15]  Stochastic stability of sectional-Anosov flows , 2015, 1505.01761.

[16]  S. Galatolo,et al.  Decay of Correlations, Quantitative Recurrence and Logarithm Law for Contracting Lorenz Attractors , 2017, Journal of Statistical Physics.

[17]  José F. Alves,et al.  Statistical stability and limit laws for Rovella maps , 2012, 1205.5639.

[18]  Roger J. Metzger,et al.  Sinai-Ruelle-Bowen measures for contracting Lorenz maps and flows , 2000 .

[19]  R. Costantino,et al.  Can noise induce chaos , 2003 .

[20]  I. Nisoli.  How does noise induce order , 2020, 2003.08422.

[21]  Mike Todd,et al.  Thermodynamic Formalism for Contracting Lorenz Flows , 2009, 0911.4111.

[22]  Ichiro Tsuda,et al.  Noise-induced order , 1983 .

[23]  M. Rasmussen,et al.  A random dynamical systems perspective on stochastic resonance , 2015, 1510.06973.

[24]  John Guckenheimer,et al.  A Strange, Strange Attractor , 1976 .