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Journal of Theoretical
and Applied Mechanics

48, 4, pp. 871-896, Warsaw 2010
APPLICATION OF ARTIFICIAL NEURAL NETWORKS IN PARAMETRICAL INVESTIGATIONS OF THE ENERGY FLOW AND SYNCHRONIZATION
Artur Dąbrowski, Anna Jach, Tomasz Kapitaniak
Technical University of Lodz, Division of Dynamics, Łódź, Poland
e-mail: ar2de@p.lodz.pl; anna.jach@p.lodz.pl; tomaszka@p.lodz.pl
Dynamics of nonlinear systems is a very complicated problem with many aspects to be recognized. Numerous methods are used to investigate such systems. Their careful analysis is connected with long-time simulations. Thus, there is great need for methods that would simplify these processes. In the paper, an application of Artificial Neural Networks (ANNs) supporting the recognition of the energy flow and the synchronization with use of Impact Maps is introduced. This connection applies an idea of the Energy Vector Space in the system with impacts. An energy flow direction change with the synchronization as a transitional state is shown. A new type of the index allowing one to control the system dynamic state is introduced. Results of the numerical simulations are used in the neural network teaching process. Results of a comparison of the straight impact map simulation and the neural network prediction are shown. Prediction of system parameters for the energy flow synchronization state with use of the neural network is presented.
Key words: nonlinear dynamics, chaos synchronization, artificial neural networks
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