Abstract
This paper describes the design and implementation of a Chua double-scroll circuit to demonstrate chaos in dynamical systems to students in a graduate course in order to enhance their visualization and understanding of strange attractor and Feigenbaum bifurcation trees.Teaching dynamical systems (i.e., nonlinear systems that can exhibit chaos) is often considered difficult because of the mathematical modeling involved and the inclusion of the fourth strange-attractor state, in addition to the traditional point stability, cyclic stability, and toroidal stability, as found in dynamic systems. A graduate course has been offered at the University of Manitoba for many years to provide both (i) a unified theory of fractal dimensions, together with many practical implementations of algorithms to compute the fractal dimensions, including the Rényi dimension spectrum that is required for characterization of the strange attractors using multifractal analysis.Leon Chua developed a simple nonlinear circuit capable of producing a rich collection of dynamic phenomena, ranging from fixed points to cycle points, standard bifurcations (period doubling), other standard routes to chaos, and chaos itself. The reason for selecting this specific circuit as a class demonstration tool is threefold: (i) the circuit has an analytical model and can be simulated, (ii) the circuit is implementable using available commercial off-the-shelf components, and (iii) the signals in the circuit can be acquired without affecting and altering its operation significantly.This paper describes the architecture, implementation, verification, and testing of the Chua system, as well as an analysis of the data obtained during the current phase of the development. Although there are many possible implementations of Chua’s circuit, our implementation has several innovative design features to make it more applicable to enhance students’ learning in the classroom.
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