Identification of Chua’s Chaotic System Based on Radial Basis Function Neural Network

The use of linear models has always been common practice in science and engineering. A good linear model, however, describes the dynamics of the system only in the neighborhood of the particular operating point for which the model was derived. The need a broader picture of the dynamics of real systems has prompted the development and use of dynamical which include the nonlinear interactions observed in practice. For very complex dynamical systems in particular, the linear models approach to modeling based on using elementary laws to determine the differential or difference equations describing he observed dynamical behavior, is often impossible to follow. In this context, the chaos theory is a relevant research topic. Chaos is a seemly random process generated in some nonlinear dynamical systems that are extremely sensitive to the changes of initial conditions. Chaos is fully deterministic and based on fixed rules that involves no elements of chance. This fact implies that the behavior of many phenomena that were considered random can be explained in terms of simple deterministic laws. However, the study of chaos has raised many interesting questions about highly complicated nonlinear systems generally. In recent years, artificial neural networks have developed increasing popularity for time series prediction and system identification. Considerable interest has been evident in the radial basis function neural networks (RBF-NN) as an alternative to the traditional multilayer perceptron architecture in neural networks applications. The RBF-NN is an architecture in which only a part of the nodes are affected by given input. The RBF-NN presents attractive characteristics, such as possibility of faster training times when the training task was formulated as a linear optimization process, local mapping, and equivalence functional with fuzzy inference system [1]. In this paper, the experimental data of a chaotic Chua’s system [2], [3] are collected and analyzed. These data are also utilized by a system identification procedure based on a RBF-NN [4], [5], [6]. In the full paper, the results of identification procedure based on RBF-NN are shown and discussed. In this context, the implementation and simulation of chaos theory, neural networks and systems identification techniques are relevant and emergent research topics with several applications in computational biology and bioinformatics, such as artificial life, analysis and synthesis of complex biological data, protein modeling, optimization of experimental designs, neurobiology, computer modeling of dynamic biological system, and others.