Arduino-based chaotic generator with polar attractor

Abstract

The paper addresses the design of methodological frameworks to construct a chaotic system with a predefined attractor. These frameworks are based on an algebraic attractor equation, which defines a set of system state coordinates in the phase plane and the interrelations between them. We consider using polar curves equations to describe a system attractor, but it is also possible to use equations in other coordinate systems. In all cases, one should define the interrelations between system state variables and the attractor’s coordinates as some algebraic dependencies. Differentiating these dependencies with respect to time yields the equations of motion for a new dynamical system describing motion along the horizontal and vertical axes. Due to the strong dependency between system state variables and attractor coordinates, it is possible to construct a novel dynamical system with separate and interconnected channels. Such systems can be implemented in continuous and discrete time domains using various analog and digital devices and elements. We demonstrate the application of our approach by designing a chaotic system based on the well-known Mackey-Glass equation and a desired cardioid-like attractor implemented on an Arduino Due board. Our studies show hidden chaos in the designed system while the desired attractor is formed.