Realization of multiscroll chaotic attractors by using current–feedback operational amplifiers
R. Trejo–Guerraª, E. Tlelo–Cuautleª, C. Sánchez–Lópezb, J.M. Muñoz–Pachecoc, and C. Cruz–Hernándezd
ª INAOE, Electronics Department, Luis Enrique Erro 1, Tonantzintla, Puebla, 72840 Mexico.
b UAT, Department of Electronics Engineering, Calzada Apizaquito, Apizaco, Tlaxcala, 90300 Mexico.
c UPP, Electronics and Telecommunications Department, Puebla, 72640 Mexico.
d CICESE, Electronics and Telecommunications Department, Km. 107, Carretera Tijuana–Ensenada, 22860 Ensenada, B.C., Mexico.
]]>Recibido el 8 de marzo de 2010
Aceptado el 21 de mayo de 2010
Abstract
Multiscroll chaotic attractors are physically implemented by using commercially available current–feedback operational amplifiers (CFOAs). The values of the circuit elements are obtained systematically by a proposed technique based in the saturation of the CFOA to create Piece–Wise Linear (PWL) functions. Herein the technique is verified by Spice simulations and in experimental form by using CFOAs to generate n–scroll attractors in a systematic way. Lyapunov exponents are given to prove the chaotic behavior.
Keywords: n–scroll attractors; Chua's circuit; break point; Lyapunov exponent; CFOA; PWL function.
Resumen
Se realiza la implementacion física de atractores caóticos de múltiples enrollamientos por medio del circuito comercial denominado amplificador operacional retroalimentado en corriente (CFOA). Los valores de los elementos del circuito son obtenidos sistemáticamente por medio de una técnica propuesta basada en la saturación del CFOA para generar funciones lineales a tramos (PWL functions). En este punto, la técnica es verificada por medio de simulaciones en Spice, así como de manera experimental utilizando CFOAs para generar atractores de n–enrollamientos de forma sistemática. Se presentan los exponentes de Lyapunov para corroborar el comportamiento caótico.
]]> Descriptores: Atractores n–enrollamientos; circuito de Chua; punto de quiebre; exponente de Lyapunov; CFOA; función lineal a tramos.
PACS: 05.45.Pq; 05.45.Pq; 84.30.Ng; 07.50.Ek; 84.30.–r; 01.50.Pa
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Acknowledgment
This work is supported by CONACyT–MEXICO through the scholarship 204229 and the project numbers 48396–Y, J49593–Y, P50051, Promep UATLX–PTC–088 and by Consejería de Innovation, Ciencia y Empresa, Junta de Andalucía Spain, under the project TIC–2532. The second author acknowledge the CONACyT sabbatical leaves program for his stay at University of California at Riverside during 2009–2010. The third author thanks the support of the JAE–Doc program of CSIC, co–funded by FSE, Spain. We also acknowledges the participation of Roberto Toledo in the realization ofthe experiments.
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