Affiliation:
1. Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10 I-50019 Sesto Fiorentino, Italy
Abstract
In this paper, we consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval [S. Lepri, Chaotic fluctuations in graphs with amplification, Chaos, Solitons & Fractals 139 (2020) 110003]. We determine the conditions for having fat-tailed invariant measures by considering approximate solution of the Perron–Frobenius equation for generic graphs. An analogy with the statistical mechanics of a directed polymer is presented that allows for a physically appealing interpretation of the statistical regimes. The connection between non-Gaussian statistics and the generalized Lyapunov exponents [Formula: see text] is illustrated. Finally, some results concerning large graphs are reported.
Publisher
World Scientific Pub Co Pte Ltd
Subject
General Physics and Astronomy,General Mathematics