An exhibition of a rich variety of periodic attractors through alternation in elemental order of series LCR-type resonant circuits

Abstract

In this work, we propose a number of systematic experiments performed on series LCR-type linear resonant circuits driven by a square wave input voltage source to generate beautiful images of periodic attractors on the screen of an oscilloscope by altering circuit’s elemental order. Besides, we also indicate how such simple linear circuits can be extended to perform numerical simulations by incorporating the mathematical of logarithmic spiral. The numerical simulation outcomes are in agreement with the laboratory results. This work could be useful in demonstrations of phase flow in a linear dynamics/nonlinear dynamics course and will pave the way to easier understand papers in nonlinear dynamics of nonlinear electronic circuits with both experimental and numerical results like Grosu et al. (Phys Rev Lett 100(23):234102, 2008). To the best of our knowledge, this work is innovative of its kind giving a prescription to present an exhibition of a rich variety of periodic attractors. We also propose that the present work has the potential to be used as classroom demonstration in topics like resonant circuits, damped harmonic oscillators, oscilloscopes, Lissajous figures, phase portraits, periodic attractors or an exciting experiment in the advance level physics and engineering laboratories utilizing such simple circuitry.