May–Wigner transition in large random dynamical systems. (27th September 2017)

• Record Type: Journal Article
• Authors: Ipsen, J R
• Is Part Of: Journal of statistical mechanics. (2017:Sep.)
• Publication Date: 2017-09-27
• Subjects: 12 -- 7; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa8704
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We consider stability in a class of random non-linear dynamical systems characterised by a relaxation rate together with a Gaussian random vector field which is white-in-time and spatial homogeneous and isotropic. We will show that in the limit of large dimension there is a stability-complexity phase transition analogue to the so-called May–Wigner transition known from linear models. Our approach uses an explicit derivation of a stochastic description of the finite-time Lyapunov exponents. These exponents are given as a system of coupled Brownian motions with hyperbolic repulsion called geometric Dyson Brownian motions. We compare our results with known models from the literature.