Evolutionary Identification of Chaotic System

Abstract

Synthesis, identification and control of complex dynamical systems are usually extremely complicated. When classics methods are used, some simplifications are required which tends to lead to idealized solutions that are far from reality. In contrast, the class of methods based on evolutionary principles is successfully used to solve this kind of problems with a high level of precision. In this paper an alternative method of evolutionary algorithms, which has been successfully proven in many experiments like chaotic systems synthesis, neural network synthesis or electrical circuit synthesis. This paper discusses the possibility of using evolutionary algorithms for the identification of chaotic systems. The main aim of this work is to show that evolutionary algorithms are capable of the identification of chaotic systems without any partial knowledge of internal structure, i.e. based only on measured data. Two different evolutionary algorithms are presented and tested here in a total of 10 versions. Systems selected for numerical experiments here is the well-known logistic equation. For each algorithm and its version, repeated simulations were done, amounting to 50 simulations. According to obtained results it can be stated that evolutionary identification is an alternative and promising way as to how to identify chaotic systems.