2017/05/23 by Jacek Grela · 21 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applied mathematics #Complex Systems and Time Series Analysis #Computer science #Differential equation #Eigenvalues and eigenvectors #Gaussian #Limit (mathematics) #Linearization #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Ordinary differential equation #Physics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Transient (computer programming) #Transient response #cond-mat.dis-nn #cond-mat.stat-mech #math-ph #math.MP #nlin.CD
paper · pdf · doi:10.1103/physreve.96.022316
published in Physical review. E 96(2), 022316 (American Physical Society) · 9 pages, 5 figures
arxiv created 2017/05/23 · openalex publication_date 2017/08/16 · arxiv updated 2017/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study transient behavior in the dynamics of complex systems described by a set of nonlinear ordinary differential equations. 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 behavior as connected to the eigenvectors and encoded in a nonorthogonality matrix T0. 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 T0 limit where it describes a normal matrix.