SIMPLE SELF-INSTRUCTIONAL MODULES BASED ON CHAOTIC OSCILLATORS: FEW BLOCKS GENERATING MANY PATTERNS

Abstract

Chaotic circuits have been widely used in the teaching of nonlinear dynamics disciplines, where a common practice is pedagogically based on the circuit point of view. Chua's circuit is the most popular platform for the demonstration of its components with rich dynamical patterns. However, engineering students majoring in control systems are more familiar with feedback systems rather than physical electronics with nonlinear components. This may lead to some difficulty in understanding the nonlinear properties of Chua's circuit, at least on first sight. This paper provides an alternative approach to teaching and learning chaotic oscillators by using the inherent understanding of feedback systems with simple modules at the undergraduate level. Utilizing the idea of chaotification, which means to make a nonchaotic module chaotic, the modules consist of only four blocks yet can generate more than thirty types of chaotic patterns via their various combinations. Conceptually, the blocks can be assembled as various mixed-mode chaotic circuits. Functionally, the blocks are easy-to-use in a Simulink-like fashion. Structurally, they are a LEGO-like educational kit. With low-cost implementation employing a few op-amps for each block, the newly proposed modules are simple, self-instructional and suitable for teaching and training students in school laboratories and in experimental environments.