THE CATEGORIZATION OF THE CHAOTIC MAPS WITH STANDPOINT OF THE ECOLOGIES

Abstract

At present in ecologies for mathematical models use the systems of chaotic maps. Presence deterministic (dynamic) chaos in such systems define with positions of the global largest Lyapunov exponent λ_1. The chaos is present when λ_1>0 (when execution of some additional conditions). When performing the studies for finding of the spectrum global and local Lyapunov exponent was used QR-method. Using QR-method were organized studies of the large number of chaotic maps however in article as example are considered only two such maps. When undertaking the studies was found that als such chaotic maps possible to refer to two classes (the class I and class II). Systems from class I have a positive largest global Lyapunov exponent. Herewith local largest Lyapunov exponents can take zero and negative values. The systems from class II also have a positive global largest Lyapunov exponent. However chaotic maps from class II have only positive values for local largist Lyapunov exponents. The study of the large number of the chaotic maps from class I and from class II has shown that majority maps from class II it is impossible adequately forecast with the help of the known presently methods of the forecasting (even on one point ahead). That is to say if ecological model is based on chaotic maps from class II that forecast in most cases not possible. For possibility of the adequate forecast it is necessary to use the ecological models built on base of the chaotic maps from class I. The purpose of the undertaking the scientific studies. The purpose of the studies consisted in creation to principal new categ0rizatiom of the chaotic maps. The purpose of the studies consisted in that to show that exists two classes of such chaotic maps (the class I and II), from which maps of the class II it is impossible forecast when use known an present time methods of the forecasting.