Universality of chaotic rare fluctuations in a locally coupled phase map model

Chaotic fluctuations of the order parameter in a coupled two-dimensional phase map model are numerically investigated. We discuss the system-size N dependence of the statistical properties of rare fluctuations observed in the transition range between the quasiordered chaotic state and the fully developed one. It is found that the normalized probability distribution function (PDF) has a unique functional form irrespective of N. The asymptotic form of the PDF is discussed in connection with the universal distribution for correlated systems proposed by Bramwell et al. [Nature (London) 396, 552 (1998)]. Moreover, it is observed that the power spectrum PN(ω) of rare fluctuations asymptotically takes the power-law form PN(ω)～ω -(1 + α) (α=0.6 ～ 0.7) irrespective of N. This result suggests that the temporal correlation decays as a stretched exponential