statistical symmetry
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2001 ◽  
Vol 11 (10) ◽  
pp. 2675-2682 ◽  
Author(s):  
ELENA S. DIMITROVA ◽  
OLEG I. YORDANOV

As a result of the recent finding that the Lorenz system exhibits blurred self-affinity for values of its controlling parameter slightly above the onset of chaos, we study other low-dimensional chaotic flows with the purpose of providing an approximate description of their second-order, two-point statistical functions. The main pool of chaotic systems on which we focus our attention is that reported by Sprott [1994], generalized however to depend on their intrinsic number of parameters. We show that their statistical properties are adequately described as processes with spectra having three segments all of power-law type. On this basis we identify quasi-periodic behavior pertaining to the relatively slow process in the attractors and approximate self-affine statistical symmetry characterizing the fast processes.


1991 ◽  
pp. 17-22
Author(s):  
Arthur L. Loeb
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1985 ◽  
Vol 38 (1-2) ◽  
pp. 371-391 ◽  
Author(s):  
Joseph L. Birman ◽  
H. -R. Trebin

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