Numerical Calculation Of Lyapunov Exponents In Various Nonlinear Chaotic Systems

Abstract In this paper we study the meaning and importance of Lyapunov exponents through methods of analysis of experimental data applied in physics and especially in chaotic circuits. The Lyapunov exponents play a very important role in detecting chaos which occurs in many areas of science and technology. So the question belongs to the theory of chaotic dynamical systems and generally all dynamical systems which should analyzed correctly and accurately to obtain the correct conclusions regards Lyapunov exponents. The purpose of the study is to find the Lyapunov exponents for various dynamical systems and the explanation of the results for the dynamic behavior of each system. We also present applications science where Lyapunov exponents play an important role in explaining the main algorithms to calculate these exponents under different implementation and different computer packages.