Searching the structure of couplings in a chaotic maps ensemble by means of neural networks

Abstract

The purpose of this work is development and research of an algorithm for determining the structure of couplings of an ensemble of chaotic self-oscillating systems. The method is based on the determination of causality by Granger and the use of direct propagation artificial neural networks trained with regularization. Results. We have considered a method for recognition structure of couplings of a network of chaotic maps based on the Granger causality principle and artificial neural networks approach. The algorithm demonstrates its efficiency on the example of small ensembles of maps with diffusion couplings. In addition to determining the network topology, it can be used to estimate the magnitue of the couplings. Accuracy of the method essencially depends on the observed oscillatory regime. It effectively works only in the case of homogeneous space-time chaos. Discussion. Although the method has shown its effectiveness for simple mathematical models, its applicability for real systems depends on a number of factors, such as sensitivity to noise, to possible distortion of the waveforms, the presence of crosstalks and external noise etc. These questions require additional research.

Keywords

• dynamical chaos
• artificial neural networks
• ensembles of maps
• couplings structure identification