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

 

J. M. Muñoz–Pacheco*¹, E. Tlelo–Cuautle²

 

^1,2 Department of Electronics, INAOE, Luis Enrique Erro No. 1, Tonantzintla, Puebla, 72840 MEXICO; Tel/Fax: 52–222–2470517; *E–mail: mpacheco@inaoep.mx, e.tlelo@ieee.org

 

ABSTRACT

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.

Keywords: Chaos, 2D–n–scroll attractors, behavioral modeling, circuit synthesis, opamp.

 

RESUMEN

El presente artículo introduce una guía para sintetizar sistemas caóticos en 2D a través de descripciones de alto nivel. El objetivo de esta investigación es sintetizar sistemas caóticos de 2D–n–enrollamientos basados en funciones saturadas con multisegmentos. La nueva metodología para síntesis de circuitos se desarrolla en tres niveles jerárquicos. Primero, el oscilador caótico en 2D se simula numéricamente a nivel de sistema electrónico aplicando variables de estado y aproximación lineal a tramos. Segundo, los niveles de excursión de las señales caóticas se escalan para controlar los puntos de rompimiento y las pendientes de las funciones saturadas dentro de valores prácticos. Adicionalmente, se desarrolla un escalamiento en frecuencia de los atractores caóticos de 2D–n–enrollamientos. Finalmente, las funciones saturadas de corriente y voltaje se sintetizan usando modelos en Verilog–A de amplificadores operacionales para que de esta manera se sintetice un sistema caótico en 2D usando amplificadores operacionales para generar atractores de 2D–n–enrollamientos. Los resultados numéricos se confirman con simulaciones en H–SPICE para mostrar la utilidad del enfoque de síntesis propuesta.

 

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Acknowledgment

J.M. Muñoz–Pacheco acknowledges CONACyT for support granted through Ph. D. scholarship #204409. This research is supported by CONACyT/MEXICO under project number 48396–Y.

 

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