Chaotic Map Construction From Common Nonlinearities and Microcontroller Implementations

Abstract

This work presents novel discrete-time chaotic systems with some known physical system non-linearities. Dynamic behaviors of the models are examined with numerical methods and Arduino microcontroller-based experimental studies. Many new chaotic maps are generated in the form of x(k + 1) = rx(k) + f(x(k)) and high-dimensional chaotic systems are obtained by weak coupling or cross-coupling the same or different chaotic maps. An application of the chaotic maps is realized with Arduino for chaotic pulse width modulation to drive electrical machines. It is expected that the new chaotic maps and their microcontroller implementations will facilitate practical chaos-based applications in different fields.