A Methodology for the Teaching of Dynamical Systems Using Analogous Electronic Circuits

Abstract

The behaviour of dynamical systems can be reproduced from analogous electronic circuits, which allows the study of many interesting phenomena associated with them using inexpensive and versatile electronic components easily found on the market. This paper proposes a methodology to develop didactic platforms for the study of dynamical systems based on analogous electronic circuits. Presented here are the design and implementation of three electronic circuits that mimic natural chaotic systems: the forced Duffing system, the Lorenz system and the Rössler system.

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

“…The design of the analogous Chua's circuit herein, is based on the methodology described in [22]. The sim- plified Chua's circuit described in (3) is simulated, aiming to estimate the maximum amplitudes of the output signals.…”

“…Since the dynamics of the Chua's circuit is governed by a set of differential equations, it can be electronically emulated by an analogous electronic circuit based on weighted analog integrators [22]. The nonlinear function of Chua's diode can be approached by line segments generated by polarized diodes in an inverter amplifier.…”

The Negative Side of Chua's Circuit Parameter Space: Stability Analysis, Period-Adding, Basin of Attraction Metamorphoses, and Experimental Investigation

“…The analogous Chua's circuit used in the experiments is shown in Fig. 13, and its design is based on the methodology described in [Rocha et al, 2006] such that the amplitudes of all output signals are restricted to ±2 V considering α = −4.00, β = −2.00, a = −8/7, and b = −5/7. The linear network of conventional Chua's circuit is emulated by analog-inverting weighted integrators with the four op-amps TL074, while the threesegmented piecewise-linear curve of Chua's nonlinearity is synthesized by using an inverter amplifier TL071 with switched gain by polarized diodes.…”

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

“…2 in order to obtain the analogous Chua's circuit. The methodology proposed by Rocha et al [11] is used to design this analogous circuit, which is based in the dimensionless approach of the Chua's system where equivalent parameter configurations are eliminated grouping the seven original parameters R , C 1 , C 2 , L, m 0 , m 1 , and B p into only four dimensionless groups α = C 2 /C 1 , β = R 2 C 2 /L, a 0 = R m 0 , and a 1 = R m 1 . 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).…”