MayWigner transition in large random dynamical systems
Abstract
We consider stability in a class of random nonlinear dynamical systems characterised by a relaxation rate together with a Gaussian random vector field which is whiteintime and spatial homogeneous and isotropic. We will show that in the limit of large dimension there is a stabilitycomplexity phase transition analogue to the socalled MayWigner transition known from linear models. Our approach uses an explicit derivation of a stochastic description of the finitetime 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.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 September 2017
 DOI:
 10.1088/17425468/aa8704
 arXiv:
 arXiv:1705.05047
 Bibcode:
 2017JSMTE..09.3209I
 Keywords:

 Mathematical Physics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics;
 Mathematics  Probability
 EPrint:
 14 pages, 1 figure. to appear in J. Stat. Mech