Mathematical Problems in Engineering 
Volume 2007 (2007), Article ID 83893, 16 pages
doi:10.1155/2007/83893
Research Article

Inductorless Chua's Circuit: Experimental Time Series Analysis

R. M. Rubinger,1 A. W. M. Nascimento,1 L. F. Mello,1 C. P. L. Rubinger,1 N. Manzanares Filho,2 and H. A. Albuquerque3

 1Instituto de Ciências Exatas, Universidade Federal de Itajubá, Itajubá 37500-903, MG, Brazil
2Instituto de Engenharia Mecânica, Universidade Federal de Itajubá, Itajubá 37500-903, MG, Brazil
3Departamento de Física, Centro de Ciências Tecnológicas, Universidade do Estado de Santa Catarina, Joinville 89223-100, SC, Brazil
Received 8 September 2006; Revised 6 November 2006; Accepted 11 February 2007

Recommended by José Manoel Balthazar

Abstract

We have implemented an operational amplifier inductorless realization of the Chua's circuit. We have registered time series from its dynamical variables with the resistor R as the control parameter and varying from 1300 Ω to 2000 Ω. Experimental time series at fixed R were used to reconstruct attractors by the delay vector technique. The flow attractors and their Poincaré maps considering parameters such as the Lyapunov spectrum, its subproduct the Kaplan-Yorke dimension, and the information dimension are also analyzed here. The results for a typical double scroll attractor indicate a chaotic behavior characterized by a positive Lyapunov exponent and with a Kaplan-Yorke dimension of 2.14. The occurrence of chaos was also investigated through numerical simulations of the Chua's circuit set of differential equations.