动力系统中确定性混沌的泛量化
Universal quantification for deterministic chaos in dynamical systems
摘要：
确定性混沌的细胞动力学系统模型能够精确量化舍入误差增长，即，连续动态系统数学模型的数字计算机实现中的确定性混沌。该模型预测如下：（a）相空间轨迹（奇异吸引子）时，解决了作为计算机精度的函数具有内在的对数螺旋曲率与准周期彭罗斯平铺模式的内部结构。(b)确定性混沌的普适常数被确定为每个计算步骤的稳态分数舍入误差k，等于1 /sqr（tau）（=0.382），其中tau是黄金平均值。(c)费根鲍姆的普适常数a和d是k的函数，此外，表达式2（a**2）=（pie）*d量化了奇异吸引子的分形几何的稳态有序出现。(d)混沌动力系统的功率谱服从普遍而唯一的统计正态分布的逆幂律形式。
英文摘要：
A cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth,i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model predicts the following: (a) The phase space trajectory (strange attractor) when resolved as a function of the computer accuracy has intrinsic logarithmic spiral curvature with the quasiperiodic Penrose tiling pattern for the internal structure. (b) The universal constant for deterministic chaos is identified as the steady-state fractional round-off error k for each computational step and is equal to 1 /sqr(tau) (=0.382) where tau is the golden mean. (c) The Feigenbaum's universal constants a and d are functions of k and, further, the expression 2(a**2) = (pie)*d quantifies the steady-state ordered emergence of the fractal geometry of the strange attractor. (d) The power spectra of chaotic dynamical systems follow the universal and unique inverse power law form of the statistical normal distribution.
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