An inductor-free realization of the Chua’s circuit based on electronic analogy

Abstract

Although literature presents several alternatives, an approach based on the electronic analogy was still not considered for the implementation of an inductor-free realization of the double scroll Chua's circuit. This paper presents a new inductor-free configuration of the Chua's circuit based on the electronic analogy. This proposal results in a versatile and functional inductorless implementation of the Chua's circuit that offers new and interesting features for several applications. The analogous circuit is implemented and used to perform an experimental mapping of a large variety of attractors.

Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua’s circuit behavior

“…The behavior of the analogous version of the Chua's circuit proposed by Rocha and Medrano [7] is experimentally characterized using usual laboratories techniques for investigation of nonlinear phenomena. These techniques, normally based in the use of oscilloscopes and sophisticated measurement equipments, are adapted to LabVIEW, which provides an adequate Fig.…”

“…In this paper, the experimental characterization is realized using the analogous Chua's circuit, an inductor-free version that reproduces the dynamical behavior of the Chua's circuit with a remarkable similarity between theoretical simulations and the experimental results [7]. The three first-order differential equations that describe the Chua's circuit are emulated by analog weighted electronic integrators, which are adequately interconnected as shown in Fig.…”

“…Although the number of components used to implement this analogous circuit is larger than other Chua's oscillator configurations, it offers new and interesting features for comfortable measurements using an acquisition board (DAQ). The three state variables are accessible and can be directly acquired by a DAQ, since they are explicitly available as voltage signals, which amplitudes and frequencies are independently [7]. Thus, the characteristics of the output signals of the analogous Chua's circuit can be adjusted according to DAQ specifications.…”

“…Since its initial proposal, the Chua's circuit is intensely investigated and has been accepted as paradigm for study of important features of nonlinear systems, once it exhibits a very complex dynamical behavior in spite of its simplicity [4]. It still presents a novel and rich scenario formed by a large variety of homoclinic orbits and bifurcations [5], periodic structures [6], and distinct chaotic attractors [7].…”

“…This paper presents an automatized analysis of the experimental behavior of the analogous version of the Chua's circuit proposed by Rocha and Medrano [7] using the LabVIEW, an integrated environment for development of applications related to measurements, tests and control. Although several possibilities can be used to investigate nonlinear phenomena, this work considers methods based in the analysis of times series produced by the circuit, which are captured by a low expensive data acquisition system.…”