Modeling And Simulation Of Chaotic Behavior

Modeling and Simulation of Chaotic Behavior
Gilberto Sánchez Mares(1), Norman Andres Herrera Hernández(1)
1.

Universidad Politécnica de Aguascalientes, Paseos de San Gerardo No. 207, 4421400ext. 1441
gilberto_gsm@hotmail.com, norman_andres09@hotmail.com

ABSTRACT:
Chaos is a stationary behavior of a dynamical system and its main characteristic is the sensitivity to initial conditions.This type of system is being considered for various areas of knowledge such as optics, mathematics, physics,
telecommunications, medicine and among others. This paper presents one of the most usedelectronic circuits for the
study of chaotic oscillators, the so called Chua´s Circuit, proposed by Leon Chua, this oscillator wins popularity due
to the large number of nonlinear behavior that occurswhen the parameter values changes. The main objective is to
analyze the above circuit, based on the mathematical modeling to understand h ow it works and some of its most
important features, as thegreat sensitivity to the variation of initial conditions and the peculiar graph (attractor)
illustrating the peculiar behavior.
Key words: Chaotic Attractor, Chua´s Circuit, Nonlinear SystemREFERENCES AND LINKS
[1] Razminia, A., Sadrnira M. A., Chua´s Circuit Regulation Using a Nonlinear Adaptive Feedback Technique,
World Academy of Science. 3 4, (2007).

1. Introduction
Chaos theory incontrol systems are defined as a stationary behavior of a dynamical system, behavior that isn´t an
equilibrium point and isn´t periodical. The so called Chua´s Circuit is a nonlinear modelrepresenting dynamic
behavior of the chaotic type. This circuit consists of four linear elements: inductor (L), resistor (R), two capacitors
(C1) and (C2); and a nonlinear element: the Chua´s diode (Fig. 1a)) .

Fig. 1. a) Chua´s Circuit y b) Chua´s Attractor.

2. Development and Results
2.a. Development
The project has been developed in two sections; the first consist of modeling the circuit...