Análisis de atractores caóticos por medio de exponentes de Lyapunov para variaciones resistivas en un circuito Chua (2021)
There are several applications for chaotic circuits, one of the best-known todays is the encryption of information in the communications area. However, with the passage of time, the possibility of finding new functions for these systems has been investigated, specifically, the option of including sensors or resonant systems of the LC type based on the consideration that the response of a chaotic system is extremely sensitive to changes in its initial conditions. Even so, the response of these systems are chaotic attractors, so the need arises to find a numerical criterion to be able to differentiate these figures in a quantitative way. According to this, the degree project presented in this document seeks to evaluate whether it is possible to use the Lyapunov exponents as the means to differentiate each one of the attractors generated by a Chua-type chaotic circuit with variants in its resistive component. For this, a group of simulations and physical tests were generated that culminated in the implementation of a Chua circuit with adjustments focused on setting the initial parameters of each measurement to generate repeatability in each variant of the system. Subsequently, the data obtained were processed to find and associate three representative values of the Lyapunov exponents to each attractor. As a result, it was established that, within the coefficients found, there are values that are repeated for taking data from the same scenario. Additionally, it was evidenced that it is possible to differentiate the type of attractor obtained by means of the equality of two of the representative exponents found.