Implementation of software that calculates the Lyapunov exponents in nonlinear systems

The irregular and unpredictable time evolution of many nonlinear systems has been called chaos. Chaos occurs in many nonlinear systems. Main characteristic of chaos is that system does not repeat its past behavior. In spite of their irregularity, chaotic dynamical systems follow deterministic equations. The unique characteristic of chaotic systems is dependence on the initial conditions sensitively. There are various methods for detecting chaos. Lyapunov exponents measure the average exponential divergence or convergence of nearby initial points in the phase space of dynamical system. A positive Lyapunov exponent is a measure of average exponential divergence of two nearby trajectories whereas a negative Lyapunov exponent is a measure of the average exponential convergence of two nearby trajectories. Positive Lyapunov exponent is an indication that the system is chaotic. In this thesis, a software for estimating Lyapunov exponents of nonlinear systems has been designed. The Lyapunov exponents are used to detect chaos in nonlinear systems. Keywords : Chaos, Lyapunov Ecponents, Calculation of Lyapunov Exponents