Chaotic fluctuations in graphs with amplification

Stefano Lepri

Chaos, Solitons & Fractals, 2020, vol. 139, issue C

Abstract: We consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval. We investigate the possibility of having power-law tails in the invariant measure by approximate solution of the Perron-Frobenius equation and discuss the connection with the generalized Lyapunov exponents L(q). We then consider the case of open maps where trajectories escape and demonstrate that stationary power-law distributions occur when L(q)=r,with r being the escape rate. The proposed system is a toy model for coupled active chaotic cavities or lasing networks and allows to elucidate in a simple mathematical framework the conditions for observing Lévy statistical regimes and chaotic intermittency in such systems.

Keywords: Chaotic map; Power-law distributions; Diffusion and amplification on graphs; Generalized Lyapunov exponents (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:139:y:2020:i:c:s096007792030401x

DOI: 10.1016/j.chaos.2020.110003

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