We report a numerical study of the Taiwan stock market, in which we used three data sources: the daily Taiwan stock exchange index (TAIEX) from January 1983 to May 2006, the daily OTC index from January 1995 to May 2006, and the one-min intraday data from February 2000 to December 2003. Our study is based on numerical estimates of persistence exponent theta(p), Hurst exponent H(2), and fluctuation exponent h(2). We also discuss the results concerning persistence probability P(t), qth-order price-price correlation function G(q)(t), and qth-order normalized fluctuation function f(q)(t) among these indices
It was shown by G. Radons1 that, for a large class of one-dimensional maps, diffusion is suppressed by the presence of quenched disorder. Focusing on simple diffusive maps with discrete disorder, we investigate the behavior of the correlation functions χ1 (τ; t) and χ01 (τ; t), which arise naturally from the random walks induced by disorder of the system. Our numerical simulations show that both χ1 (τ; t) and χ01 (τ; t) decay with τ more slowly than the exponential decay, and both scale linearly with t; i.e. χ1 (τ; t) = tϕ1 (τ) and χ01 (τ; t) = tϕ01 (τ). Interestingly, we have also found that both [Formula: see text] and [Formula: see text] are mainly independent of the disorder configurations of the system.
Our numerical simulation first displays exponential increase of the mean number of attractors with N for K = 2,3,4 and 50≦ N ≦350. The mean length of attractors also increases exponentially with N for K = 2, but increases linearly with N for K = 3,4. We further found the larger the K the larger S/N value; which yields the results that the mean length and the mean number of attractors of critical random Boolean networks will decrease with larger K.
By investigating numerically a circle map with two cubic inflection points, we find that the fractal dimension D of the set of quasiperiodic windings at the onset of chaos has a variety of values, instead of a unique value like 0.87. This fact strongly suggests that a family of universality classes of D appears as the map has two various inflection points. On the other hand, at the quasiperiodic transition with the golden mean winding number, the ratios δn of the width of the mode lockings when going from one Fibonacci level to the next do not converge to a fixed value or a limit cycle in most cases. In this sense, local scaling is broken due to the interaction of the two inflection points of the map. Based on the above observations, it seems that the global scaling is more robust than the local one, at least for the maps we considered.
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