论文标题
与扩增的图表中的混乱波动
Chaotic fluctuations in graphs with amplification
论文作者
论文摘要
我们考虑了一个混乱扩散的模型，并在与间隔的分段线性图相关的图表上放大。我们通过近似perron-frobenius方程的近似解决方案来研究在不变度量中使用幂律的可能性，并与广义的lyapunov指数$ l（q）$讨论联系。然后，我们考虑了开放地图的情况，在该情况下，轨迹逃脱并证明当$ l（q）= r $时发生固定的幂律分布，而$ r $是逃生率。所提出的系统是一种用于耦合活跃混乱型或激光网络的玩具模型，并允许在简单的数学框架中阐明观察Lévy统计方案和混乱的际间歇性的条件。
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.
