Pragmatic modeling of chaotic dynamical systems through artificial neural network

Abstract

The precipitous advancements in the field of modeling of dynamical systems, which are the result of numerous relevant investigations, are the evidence of its fundamental importance. Not only does the modeling of the behavior of dynamical systems such as biological systems play an important role in the accurate perception and analysis of these systems, but it also becomes feasible to perfectly predict and control their behaviors. The results of the majority of these researches have indicated that chaotic behavior is a prevalent feature of complex interactive systems. Our achieved results indicate that artificial neural networks provide us the most efficacious means to model the underlying dynamics of these systems. In this paper, we represent the results of utilizing a specific neural network to model some famous chaotic systems such as Lorenz. The main aspect of our technique is training the neural network with a chaotic map. With this aim, at first, bifurcation diagram of the points obtained by applying Poincaré section on the time series is plotted. The specified neural network is then trained with the extracted map. We conclude the paper by evaluating the accuracy and robustness of our model. The capability of the selected neural network to model the complex behavior of dynamical systems is indeed verified, even at the presence of noise.