Chaotic fluctuations in graphs with amplification
arXiv:2006.11015 · doi:10.1016/j.chaos.2020.110003
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 . We then consider the case of open maps where trajectories escape and demonstrate that stationary power-law distributions occur when , with 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.
arXiv commentAccepted for publication in Chaos, Solitons & Fractals
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