A chaotic system with equilibria located on an open curve and its microcontroller implementation

Abstract

In this work, the implementation of a chaotic oscillator by using a microcontroller is proposed. The dynamical system, which is used, belongs to the recently new proposed category of dynamical systems with hidden attractors. In more details, the system has an infinite number of equilibrium points which is located on an open hyperbolic sine curve. By programming the microcontroller, the three most useful tools of nonlinear theory, the phase portrait, the Poincaré map and the bifurcation diagram can be produced. The comparison of these with the respective simulation results, which are produced by solving the continuous dynamical system with Runge-Kutta, verified the feasibility of the proposed method.