Assessment of Effects of a Delay Block and a Nonlinear Block in Systems with Chaotic Behavior Using Lyapunov Exponents

Evaluación del Efecto de un Retardo y una No Linealidad en Sistemas con Comportamiento Caótico Utilizando Exponentes de Lyapunov

  • Pablo César Rodríguez Gómez Universidad Distrital
  • Maikoll Andres Rodriguez Nieto Universidad Distrital
  • Jose Jairo Soriano Mendez Universidad Distrital
Keywords: Chaos, Dynamical Systems, Lyapunov Exponents, Nonlinear Characteristic. (en_US)
Keywords: Caos, Característica No lineal, Exponentes Lyapunov, Sistemas Dinámicos (es_ES)

Abstract (en_US)

Context: Because feedback systems are very common and widely used, studies of the structural characteristics under which chaotic behavior is generated have been developed. These can be separated into a nonlinear system and a linear system at least of the third order. Methods such as the descriptive function have been used for analysis.

Method: A feedback system is proposed comprising a linear system, a nonlinear system and a delay block, in order to assess his behavior using Lyapunov exponents. It is evaluated with three different linear systems, different delay values and different values for parameters of nonlinear characteristic, aiming to reach chaotic behavior.

Results: One hundred experiments were carried out for each of the three linear systems, by changing the value of some parameters, assessing their influence on the dynamics of the system. Contour plots that relate these parameters to the Largest Lyapunov exponent were obtained and analyzed.

Conclusions: In spite non-linearity is a condition for the existence of chaos, this does not imply that any nonlinear characteristic generates a chaotic system, it is reflected by the contour plots showing the transitions between chaotic and no chaotic behavior of the feedback system.

Language: English


 

Abstract (es_ES)

Contexto: Al ser los sistemas realimentados muy comunes y ampliamente usados, se han desarrollado estudios de las características estructurales bajo las cuales se genera comportamiento caótico. Estos pueden ser separados en un sistema no lineal y un sistema lineal por lo menos de tercer orden. Se han usado métodos como la función descriptiva para su análisis.


Método: Se propone un sistema realimentado a partir de un sistema lineal, un sistema no lineal y un retardo, con el fin de evaluar su comportamiento utilizando los exponentes de Lyapunov. Se evalúa con tres diferentes sistemas lineales, diferentes valores del retardo y diferentes valores para los parámetros de una característica no lineal, buscando alcanzar un comportamiento caótico.

Resultados: Se realizaron cien experimentos para cada uno de los tres sistemas cambiando el valor de algunos parámetros evaluando la influencia de los mismos en la dinámica del sistema. Se realizan y analizan gráficas de contorno que relacionan estos parámetros con el máximo exponente de Lyapunov.

Conclusiones: A pesar que la no linealidad es una condición para que exista caos, esto no implica que cualquier característica no lineal genera un sistema caótico, esto se evidencia en las gráficas de contorno mostrando las transiciones entre comportamiento caótico y no caótico del sistema realimentado.

Idioma: Inglés

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Author Biography

Pablo César Rodríguez Gómez, Universidad Distrital
Estudiante de Ingeniería Electrónica residente en la ciudad de Bogotá

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How to Cite
Rodríguez Gómez, P. C., Rodriguez Nieto, M. A., & Soriano Mendez, J. J. (2017). Assessment of Effects of a Delay Block and a Nonlinear Block in Systems with Chaotic Behavior Using Lyapunov Exponents. Ingeniería, 22(2), 240-253. https://doi.org/10.14483/udistrital.jour.reving.2017.2.a05
Published: 2017-05-05
Section
Special Section: Best Extended Articles - WEA 2016