Editorial

Abstract

Welcome to the first issue of Discrete Dynamics in Nature and Society. We are sure that you will find new and interesting information about discrete dynamics, and we invite you to contribute your own ideas to the fascinating field of Discrete Non-linear Dynamics. Over the past decades, Discrete Non-linear Dynamics has emerged as an active area of re

Some creative properties of the 2D and 3D lattice distributed interconnected chaotic oscillators and neuronal networks

“…Chaotic regimes embedded into the different types of difference equations have been demonstrated their creative properties. Application of the presented method for creative mathematical imaging, modeling of complex, living and thinking systems and especially brain specific properties presented and discussed [1,2].…”

“…It shown that use of difference equations which are related to the physicochemical laws of nature will result to the patterns in a form of rings and spirals waves ( Fig. 3 c,d) among the other patterns which are resembling naturally observed [1].…”

“…Mathematical modeling of the brain's neurons networks by interconnected oscillators with chaotic regimes is one of the effective methods to simulate brain creativity in a form of artistic images within their relation to the "brain waves" (EEG) [1,2].…”

“…Here parameter p n {X n-1 (net)} = F( , X n-1 (net)) depend from the values X n-1 (net) distributed on the lattice (net) and calculated at previous, to the considered state n, states (n-s) n, s = 1, 2,… In the simplest case X n-1 (net) just the closest to considered cell with coordinates (i,j) eight neighbors with coordinates (i-1, j-1; i+1, j; … i+1, j+1), s = 1 and F is an arbitrary chosen analytical function with parameters [1]. Computed according to (1) 2D lattice distributed sequences of 2D arrays of X n (i,j) encoded by colored palette [2].…”

“…Computed according to (1) 2D lattice distributed sequences of 2D arrays of X n (i,j) encoded by colored palette [2]. Identical approach was applied to the Henon iterative map and to the systems of difference equations obtained from the discrete chemical reactions dynamics [1]. It shown that discrete logistic equation can be used for generating colored symmetrical patterns (ornaments (Fig.…”