Regular Article

Exploring an experimental analog Chua’s circuit

¹ Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, PR, Brazil
² Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, SC, Brazil

^a e-mail: mbeims@fisica.ufpr.br

Received: 21 February 2019
Received in final form: 12 April 2019
Published online: 24 June 2019

Abstract

In this work we carry out experimental studies of the paradigmatic Chua’s circuit using an approach of the analog computation instead of performing experiments in the canonical circuit. This means that we have built an electronic circuit that integrates (analog computation), in continuous time, the equations of motion of the canonical Chua’s circuit. The equations of motion of the analogical circuit are equivalent to the canonical circuit, so that the dynamical behaviour is the same. With this approach, we successfully obtain an experimental parameter plane using the largest Lyapunov exponent (here named Lyapunov diagram), directly calculated from the experimental time series, with a good precision, so that different types of dynamical behaviours were characterized in this diagram. Results are in very good agreement with numerical simulation with an additional Gaussian noise. The approach by analog computation used here can be extended to a wide range of dynamical systems, once that the analog circuit simulates, by circuitry implementation, the dynamics of these systems from an experimental point of view.