仓本模型在“混沌边缘”的中心极限行为
Central Limit Behavior in the Kuramoto model at the 'Edge of Chaos'
摘要：
研究了仓本模型的混沌行为与中心极限定理的关系。我们计算的总和的角度在等距时间沿确定性的单振子的轨迹，我们表明，当混乱是足够强的，Pdfs的总和往往是高斯，一致的标准CLT。另一方面，当系统处于“混沌边缘”时（即在李雅普诺夫指数消失的状态下），鲁棒的$q$ -高斯吸引子自然出现，与最近证明的CLT的推广一致。
英文摘要：
We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong, the Pdfs of the sums tend to a Gaussian, consistently with the standard CLT. On the other hand, when the system is at the "edge of chaos" (i.e. in a regime with vanishing Lyapunov exponents), robust $q$-Gaussian-like attractors naturally emerge, consistently with recently proved generalizations of the CLT.
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