Graphical Interface for Obtaining Lyapunov Exponents in Fractional Order Chaotic Systems

In this article, a graphical user interface (GUI) is developed and designed in Matlab using the Guide tool, capable of solving and graphing fractional-order chaotic systems with 3 to 5 different variables, obtaining the system's Lyapunov exponents, as well as its bifurcation plot and equilibrium points. To achieve this, the numerical method based on the Adam-Bashforth-Moulton predictor-corrector is used to solve chaotic systems of the same or different fractional orders, as well as the Benettin-Wolf algorithm to obtain the Lyapunov exponents in fractional-order chaotic systems. Finally, the results of each of the simulations for two different fractional-order chaotic oscillators are presented: The Lorenz oscillator and the Chen oscillator. The importance of calculating the Lyapunov exponents and obtaining the bifurcation plot of a chaotic system lies in the fact that these results are a great indicator of whether the system has chaotic behavior with its current parameters or for a previously defined range of parameters. Similarly, it is important to know the equilibrium points of the chaotic system, as these values indicate the number of wrappings the system has, as well as being a clear indicator of the values towards which the system's oscillations tend.