Author: JESUS MANUEL MUÑOZ PACHECO

Modelado matemático de sistemas caóticos orientado a la síntesis de circuitos

JESUS MANUEL MUÑOZ PACHECO (2010)

La aplicación de modelos de comportamiento analógicos para simular el comportamiento de un sistema caótico, el circuito de Chua, el cual consiste de cinco elementos de circuito: un resistor lineal, un inductor, dos capacitores y un resistor no lineal conocido como el diodo de Chua. El último elemento es modelado por una función I-V lineal a tramos para formular un sistema de ecuaciones diferenciales dinámicas lineales. Este problema de valor inicial es solucionado aplicando el algoritmo de integración numérica Runge-Kutta para calcular una secuencia de fenómenos caóticos. Se hace énfasis en la utilidad del modelado matemático y la simulación numérica para estimar los valores de los elementos de circuito de tal forma que la síntesis del diodo de Chua pueda ser realizada directamente utilizando dispositivos activos tales como amplificadores operacionales de voltaje.

Article

INGENIERÍA Y TECNOLOGÍA

Synthesis of chaotic oscillators by applying behavioral modeling

JESUS MANUEL MUÑOZ PACHECO (2009)

This Thesis introduces a synthesis methodology to design n-scrolls chaotic

systems by means of high-level behavioral modeling, which allows easily exploring a

wide range of parameters for the n-scrolls chaotic systems and, at the same time, to

exploit specific aspects of them leading to efficient evaluation of their performance.

Therefore, the goal of the research here reported, consists in the improvement of the

analog design process for n-scrolls chaotic systems by means of the definition,

development, and demonstration of an automatic synthesis methodology, which helps

to reduce the design complexity for this class of systems and allows to exploit their

possibilities in chaos-based information systems.

The new methodology of circuit synthesis is performed by three hierarchical

levels. First, the chaotic oscillators are numerically simulated at the electronic system

level by applying state variables and piecewise-linear approximation. To speed-up

time simulation, it is implemented a procedure for the automatic control and

determination of step-size in Adams-Moulton algorithms. Second, the excursion

levels of the chaotic signals are scaled to control the breaking points and slopes of the

saturated functions within practical values. Additionally, the frequency scaling of

chaotic attractors is performed. When saturated functions have been computed, they

can be synthesized using high-level Verilog-A models. In this manner, a chaotic

oscillator is synthesized using operational amplifiers to generate n-scrolls chaotic

attractors with multiple orientations. The stability of the synthesized chaotic attractors

is determined by calculating the Lyapunov exponents using an algorithm also

proposed in this Thesis. Finally, the implementation of a CAD-tool framework for the

synthesis methodology is also reported. Numerical results are confirmed by SPICE

simulations and experimental results to show the usefulness of the proposed synthesis

approach.

This Thesis is the result of 3 years of scientific research within the Integrated

Circuit design research group of the Department of Electronics at the National

Institute of Astrophysics, Optics and Electronics in Mexico. Furthermore, the results

of this Thesis have been published in 7 Journals, 2 conference proceedings and 1

local conference.

Esta Tesis introduce una nueva metodología de síntesis enfocada en el diseño de

sistemas caóticos de n-enrollamientos aplicando modelado comportamental, el cual

permite explorar fácilmente un amplio rango de parámetros para los sistemas caóticos

de n-enrollamientos y al mismo tiempo, explotar sus aspectos específicos lo que

conduce a una evaluación eficiente de su rendimiento. Por lo tanto, la meta de la

investigación aquí reportada, consiste en mejorar el proceso de diseño analógico para

sistemas caóticos de n-enrollamientos por medio de la definición, desarrollo y

demostración de una metodología de síntesis automática la cual ayudará a reducir la

complejidad en el diseño para esta clase de sistemas y consecuentemente, permitirá

explorar sus posibilidades en aplicaciones de sistemas de información basados en

caos.

La metodología propuesta de síntesis de circuitos se ejecuta en tres niveles

jerárquicos. Primero, los osciladores caóticos son simulados numéricamente a nivel

de sistema electrónico aplicando las aproximaciones de variables de estado y

funciones lineales a trozos. Para disminuir el tiempo de simulación, se implementa

una técnica la cual permite controlar y determinar de manera automática el tamaño de

paso de integración en los algoritmos Adams-Moulton. Segundo, los niveles de

excursión de las señales caóticas se escalan a niveles prácticos para controlar los

puntos de ruptura y las pendientes de las funciones saturadas. Además, se realiza

también el escalamiento en frecuencia de los atractores caóticos; cuando las funciones

saturas se han calculado, estas pueden ser sintetizadas utilizando modelos Verilog-A.

Consecuentemente, se sintetizan los osciladores caóticos utilizando amplificadores

operacionales, los cuales generan atractores caóticos de n-enrollamientos con

múltiples orientaciones. La estabilidad de los atractores sintetizados se determina por

medio del cálculo de los exponentes de Lyapunov utilizando un algoritmo también

propuesto en este trabajo. Finalmente, la realización de la arquitectura para la

herramienta de Diseño Asistido por Computadora que soporta la estrategia de síntesis

propuesta es descrita. Los resultados numéricos son confirmados por las simulaciones

con SPICE y por realizaciones experimentales, de esta manera se muestra la utilidad

del método de síntesis propuesto.

Doctoral thesis

Chaos Circuit CAD CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA

Respuesta en frecuencia de osciladores caóticos

JESUS MANUEL MUÑOZ PACHECO (2011)

En este trabajo se presenta un experimento para obtener la respuesta en frecuencia de un oscilador caótico, utilizando equipo de medición para el análisis de espectros de señales. Los resultados experimentales concuerdan con la información teórica y matemática existente. El experimento está enfocado académicamente a diferentes áreas de la ingeniería tanto para estudiantes no-graduados como graduados.

Article

INGENIERÍA Y TECNOLOGÍA

Synthesis of n-Scroll attractors using saturated functions from High-Level simulation

JESUS MANUEL MUÑOZ PACHECO ESTEBAN TLELO CUAUTLE (2008)

Modeling and simulation of a chaotic oscillator based on saturated nonlinear functions (SNLFs) are presented for the synthesis of n-scrolls attractors. First, the oscillator is simulated at the electronic system level by applying state variables and piecewise-linear approximation. Second, the dynamic ranges are scaled to control the breaking points and slopes within practical values. Additionally, the frequency scaling of n-scrolls attractors is performed. Finally, the SNLF is synthesized using operational amplifiers to generate 2, 3, 4, 5 and 6- scrolls attractors. Theoretical results are confirmed by SPICE simulations to show the usefulness of the proposed synthesis approach.

Article

CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA

Numerical simulation of chua’s circuit oriented to circuit synthesis

ESTEBAN TLELO CUAUTLE JESUS MANUEL MUÑOZ PACHECO (2007)

The application of numerical methods based on polynomial approximation and multistep algorithms is presented to simulate the behavior of a chaotic oscillator, e.g. Chua’s circuit, which consist of five circuit elements: one linear resistor, one inductor, two capacitors and one nonlinear resistor known as Chua’s diode. The last element is modeled by an I-V piecewise-linear function to formulate a system of linear dynamic equations. This initial value problem is solved by applying numerical simulation to compute a sequence of chaotic phenomena by solving the state-variables equations describing Chua’s circuit. It is highlighted the usefulness of numerical methods to speed-up time simulation to estimate the values of the circuit elements, so that the synthesis of Chua’s diode can be realized directly using novel active devices. For instance, it is described the synthesis of Chua’s circuit using SPICE and standard CMOS integrated-circuit technology of 0.35μm, to show the control of the I-V slopes and the generation of chaotic phenomena which are in good agreement with that computed from numerical simulation.

Article

Numerical simulation State variables approach Chaotic oscillator Chua’s circuit Electronic design automation Circuit simulation CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA

Automatic simulation of 1D and 2D chaotic oscillators

ESTEBAN TLELO CUAUTLE JESUS MANUEL MUÑOZ PACHECO (2008)

A new method is introduced for automatic simulation of three kinds of chaotic oscillators: Chua’s circuit, generalized Chua’s circuit and chaotic oscillator implemented with saturated functions. The former generates the double-scroll, and the others 1D n-scroll attractors. The third chaotic oscillator is modified to generate 2D n-scrolls attractors. The oscillators are modelled by applying state variables and piecewise-linear approximation. Basically, the method computes the eigenvalues of the oscillators to begin time simulation and to make control of step-size automatically.

Article

CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA

Automatic synthesis of 2D‐n‐scrolls chaotic systems by behavioral modeling

JESUS MANUEL MUÑOZ PACHECO ESTEBAN TLELO CUAUTLE (2009)

This paper introduces the guidelines to synthesize 2D chaotic systems by means of high‐level descriptions. The aim of this investigation is to synthesize 2D‐n‐scrolls chaotic systems based on saturated functions with multisegments. The new methodology of circuit synthesis is performed by three hierarchical levels. First, the 2D chaotic oscillator is numerically simulated at the electronic system level by applying state variables and piecewise‐linear approximation. Second, the excursion levels of the chaotic signals are scaled to control the breaking points and slopes of the saturated functions within practical values. Additionally, the frequency scaling of 2D‐n‐scrolls chaotic attractors is performed. Finally, current and voltage saturated functions are synthesized using Verilog‐A models for the operational amplifiers and in this manner a 2D chaotic system is synthesized using operational amplifiers to generate 2D‐n‐scrolls attractors. Numerical results are confirmed by H‐SPICE simulations to show the usefulness of the proposed synthesis approach.

Article

Chaos 2D‐n‐scroll attractors Behavioral modeling Circuit synthesis Opamp CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA ELECTRÓNICA

Opamp-based synthesis of a fractional order switched system

ERNESTO ZAMBRANO SERRANO Jesús Manuel Muñoz Pacheco Eric Campos Cantón (2016)

"The analysis, design and circuit synthesis of a fractional order switched system is presented in this paper. That system is capable of showing chaotic oscillations with a fractional order less than three, i.e., 2.4. The dynamical system is called fractional order unstable dissipative system (FOUDS); because it consists of a switching law to display strange attractors. Its dynamical behavior is explored and a circuit synthesis system is realized considering operational amplifiers. SPICE simulations agree with the numerical results."

Article

Chaos CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA MATEMÁTICAS MATEMÁTICAS

Frequency scaling simulation of Chua’s circuit by automatic determination and control of step-size

ESTEBAN TLELO CUAUTLE JESUS MANUEL MUÑOZ PACHECO Jorge Martinez_Carballido (2007)

A procedure is introduced to speed-up time simulation of Chua’s circuit by means of determining the eigenvalues of its

state matrixes. A multistep method is applied with automatic control of step-size (h), where h is determined by the computation

of the eigenvalues of the state matrixes which change according to the slopes of Chua’s diode. It is shown that

the proposed simulation procedure enhances the estimation of the values of the circuit elements in Chua’s circuit and the

exploration on its frequency scaling behavior. Besides, it is not necessary to give an initial step-size for initializing the

simulation.

Article

Numerical simulation State variables approach Chua’s circuit Step-size control Eigenvalues CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA

OpAmp-, CFOA- and OTA-Based Configurations to Design Multi-Scroll Chaotic Oscillators

Jesús Manuel Muñoz Pacheco ESTEBAN TLELO CUAUTLE CARLOS SANCHEZ LOPEZ (2012)

Continuous time chaotic oscillators have been implemented by using several commercially available electronic devices. In this study, the generic circuit topologies based on Operational Amplifier (OpAmp), Current-Feedback Operational Amplifier (CFOA) and Operational Transconductance Amplifier (OTA), are summarized. These topologies allows an electronic designer to realize chaotic oscillators modeled with piecewise-linear functions, as it is shown herein by designing saturated function series.

Article

Multi-scroll Chaotic oscillator Circuit synthesis Operational amplifier Current-feedback operational amplifier Operational transconductance amplifier CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA ELECTRÓNICA