2022/01/04 by Théo Dessertaine, Dessertaine, Théo, Jean‐Philippe Bouchaud +1
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Stochastic processes and statistical mechanics #Opinion Dynamics and Social Influence
paper · pdf · doi:10.48550/arxiv.2201.01324
We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either v^′=\mathbbAv or \mathbbBv (with \mathbbA, \mathbbB independently drawn a rotationally invariant ensemble of N × N matrices) depending on the sign of the first component of v. We establish strong connections with the random diffusion persistence problem. When N → ∞, we find that the Lyapounov exponent is non self-averaging, i.e. one can observe apparent stability and apparent instability for the same system, depending on time and initial conditions. Finite N effects are also discussed, and lead to cone trapping phenomena.