A New Class of Circulant Chaotic Systems with Unidirectional or Mutual Coupling: Theoretical Investigation and Arduino-Based Electronic Implementation

Abstract

The study of chaotic systems with special properties addresses one of the ongoing research topics. In this paper, we introduce a new class of third-order chaotic systems possessing a cyclic symmetry obeying unidirectional or mutual coupling. These new models are built by considering nonlinearities with three, four, or five segments and are distinguished from each other by the topological structure of the associated chaotic attractor. The projection of the novel chaotic attractors on certain planes reveals their multiscroll or multiwing character. For illustration, one of these models is studied in detail using analytical and numerical methods. The mechanism giving rise to the establishment of the chaotic regime starting from the state of equilibrium under the variation of a parameter is described using bifurcation diagrams, phase portraits, basins of attraction as well as the maximum Lyapunov exponent. Several zones of parameters are identified where the model experiences two or more attractors (i.e. multistability). In order to demonstrate the practical feasibility of the proposed circulant models, a series of experimental measurements are carried out using a physical implementation with an Arduino microcontroller.