INFORMATION AND SELF-ORGANIZATION REVISITED VIA COMPLEX-VALUED FRACTIONAL BROWNIAN MOTION OF ORDER n

Abstract

Haken obtained many interesting results on information and self-organization by using Jaynes' maximum entropy principle with constraints in the form of given values of state moments up to the fourth order. The basic contention of this approach lies on the selection of these constraints, for the very reason that the result so obtained depended heavily upon them. The mean values of the state moments are quite acceptable and understandable, but why not the fifth one? In this paper, it is shown that the use of complex valued fractional Brownian motion of order n can contribute to answering this question. In addition, one examines how Haken's results are modified when the disturbing random term is not a Gaussian white noise, but a fractional Gaussian white noise of order n. The effect of such a noise on the stability of dynamical systems is analyzed. The key is that one has to consider much more state moments than when one works with Gaussian white noise.