噪声倍周期映象的临界涨落
Critical fluctuations of noisy period-doubling maps
摘要：
我们扩展了动力学系统中的准势理论，在广泛的一类倍周期映射中，计算了在弱噪声极限下干草叉分岔临界涨落的精确势。这些远离平衡的波动是由有限尺寸平均场论描述的，将它们的静态性质放在与完整图上的伊辛模型相同的普适类中。我们证明了有噪声的倍周期分岔的有效系统尺寸沿倍周期路径表现出普遍的标度行为。
英文摘要：
We extend the theory of quasipotentials in dynamical systems by calculating, within a broad class of period-doubling maps, an exact potential for the critical fluctuations of pitchfork bifurcations in the weak noise limit. These far-from-equilibrium fluctuations are described by finite-size mean field theory, placing their static properties in the same universality class as the Ising model on a complete graph. We demonstrate that the effective system size of noisy period-doubling bifurcations exhibits universal scaling behavior along period-doubling routes to chaos.
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