Restriction on the Amplitude of the Stochastic Terms - A Source of a Power Dependent Autocorrelation Function

MK Koleva

Institute of Catalysis, Bulgarian Academy of Sciences 1113 Sofia, Bulgaria
Fax: (359) 2 751 116; e-mail: mkoleva@ic.bas.bg

Proceeding of International Conference on Biomathematics:
Bioinformatics and Applications of the Stochastic Differntial-Difference Equations
Eds. H Akca, V Covachev and E Lytsin,
Publication of the Biology Departament, Faculty of Arts and Sciences,
Akdeniz University, Antalya Turkey, p.54-63, 1999.

Abstract

It has been found out that the major common proporty between the new type noise, called 1/falpha(f) (M. K. Koleva, Bulg. Chem. Ind., 69 (1998) 119) and the deterministic chaos is the restriction on the variability of the solution. The solution at the deterministic chaos is confined in the region of strange attractor which has finite volume in the phase space. The power spectra at the deterministic chaos and 1/falpha(f) noise have the same low frequency limit, namely 1/f dependence, while the high frequency limit is different. Another difference between the deterministic chaos and the 1/falpha(f) noise is that the later can comprise both a discrete and a continuous band while at the deterministic chaos the power spectra comprise only a continuous band.