English

What drives transient behaviour in complex systems?

Chaotic Dynamics 2017-08-23 v1 Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics math.MP

Abstract

We study transient behaviour in the dynamics of complex systems described by a set of non-linear ODE's. Destabilizing nature of transient trajectories is discussed and its connection with the eigenvalue-based linearization procedure. The complexity is realized as a random matrix drawn from a modified May-Wigner model. Based on the initial response of the system, we identify a novel stable-transient regime. We calculate exact abundances of typical and extreme transient trajectories finding both Gaussian and Tracy-Widom distributions known in extreme value statistics. We identify degrees of freedom driving transient behaviour as connected to the eigenvectors and encoded in a non-orthogonality matrix T0T_0. We accordingly extend the May-Wigner model to contain a phase with typical transient trajectories present. An exact norm of the trajectory is obtained in the vanishing T0T_0 limit where it describes a normal matrix.

Keywords

Cite

@article{arxiv.1705.08758,
  title  = {What drives transient behaviour in complex systems?},
  author = {Jacek Grela},
  journal= {arXiv preprint arXiv:1705.08758},
  year   = {2017}
}

Comments

9 pages, 5 figures

R2 v1 2026-06-22T19:57:43.980Z