Lévy开关不稳定性
Lévy on-off intermittency
摘要：
我们提出了一种新的形式的双稳性，Lévy on-off双稳性，它产生于乘法$α$ -接近不稳定阈值的稳定白噪声。我们研究这个问题的线性和非线性制度，理论和数值模拟，与波动增长率的干草叉分叉的情况下。我们计算的平稳分布分析和数值从相关的分数福克-普朗克方程的Stratonovich解释。我们在噪声的参数空间$(α,β)$中刻画了该系统，其中稳定性参数为$α\in (0,2)$，偏度参数为$β\in[-1,1]$。在这个参数空间中，除了研究良好的高斯情况下$α=2$五个政权被确定。三个区域位于$1<α<2$，其中噪声具有有限均值但无穷方差。它们由$β$区分，并且都在确定性不稳定阈值处显示临界转变，开关不稳定性接近开始。临界指数从平稳分布计算。每一个区域的特征在于特定形式的密度和特定的临界指数，这与高斯情况截然不同。有限个或无限个整数阶矩可以收敛，这取决于参数。在$0<α\leq 1$中发现了另外两种机制。在那里，噪声的平均值发散，并且没有临界转变发生。在一种情况下，原点总是不稳定的，与距确定性阈值的距离$μ$无关。在另一种情况下，原点相反总是稳定的，与$μ$无关。因此，我们证明了一个不稳定的非平衡，幂律分布的波动可以显示实质上不同的属性比高斯热波动，在统计和临界行为。
英文摘要：
We present a new form of intermittency, Lévy on-off intermittency, which arises from multiplicative $α$-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both theoretically and numerically, for the case of a pitchfork bifurcation with fluctuating growth rate. We compute the stationary distribution analytically and numerically from the associated fractional Fokker-Planck equation in the Stratonovich interpretation. We characterize the system in the parameter space $(α,β)$ of the noise, with stability parameter $α\in (0,2)$ and skewness parameter $β\in[-1,1]$. Five regimes are identified in this parameter space, in addition to the well-studied Gaussian case $α=2$. Three regimes are located at $1<α<2$, where the noise has finite mean but infinite variance. They are differentiated by $β$ and all display a critical transition at the deterministic instability threshold, with on-off intermittency close to onset. Critical exponents are computed from the stationary distribution. Each regime is characterized by a specific form of the density and specific critical exponents, which differ starkly from the Gaussian case. A finite or infinite number of integer-order moments may converge, depending on parameters. Two more regimes are found at $0<α\leq 1$. There, the mean of the noise diverges, and no critical transition occurs. In one case the origin is always unstable, independently of the distance $μ$ from the deterministic threshold. In the other case, the origin is conversely always stable, independently of $μ$. We thus demonstrate that an instability subject to non-equilibrium, power-law-distributed fluctuations can display substantially different properties than for Gaussian thermal fluctuations, in terms of statistics and critical behavior.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
