A GALLERY OF CHUA ATTRACTORS: PART I

Abstract

Chua Oscillator exhibits a wide variety of nonlinear behavior and has become a paradigm for theoretical and experimental investigations of chaotic systems. An initial exploration of the parameter space for the circuit shows that the system and its generalizations generates a broad range of very different strange attractors. In the work described in this paper, we constructed "a gallery" of these attractors, including patterns that have never previously been observed. We identified the regions of parameter space occupied by each attractor and the initial conditions leading to production of the attractor. System behavior was characterized using time series, FFT graphs and in some cases Lyapunov exponents. In this way we created a complex picture of chaos, which we divided into six parts. The first, we publish here. The rest of our work will be published in subsequent issues of this journal. In this first paper, we describe how to build Chua Oscillator and some of its generalizations, as proposed in the recent literature. We introduce the main features that characterize the chaotic behavior of each of these systems. Finally, we offer hints on the mechanisms underlying synchronization between pairs of coupled Chua Oscillators. The investigation of chaos allows for the emergence of a complex picture, which could improve our knowledge of these challenging phenomena in contemporary science.