Implementation of a Hyperchaotic System with Hidden Attractors into a Microcontroller

Abstract

Abstract. In this work, the implementation of a hyperchaotic 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. 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. The algorithms could be easily modified to add or substitute the hyperchaotic system.

Design and Implementation of a Microcontroller Based Active Controller for the Synchronization of the Petrzela Chaotic System

“…Two of the most used methods to resolve differential equations of chaotic systems are Euler 1st order and Runge-Kutta 4th order numerical algorithms [4,[50][51][52][53][54][55][56]. Euler is a straight-forward method, quick and it is easy to code, although its accuracy is poor.…”

“…In general, to be able to use chaotic systems in engineering applications, it is necessary to have a real implementation of them by means of analog electronic devices [48,49] or embedded systems [50]. The implementation of chaotic systems in embedded devices such as microcontrollers [50][51][52][53], digital signal processors (DSP), or field programmable gate array (FPGA) [4,[54][55][56], have advantages in comparison with the implementation of circuits with analog components such as operational amplifiers and multipliers. Some of the advantages include a higher velocity of implementation, high computational power, low power consumption and precision because the resistors and capacitors have tolerance problems, which do not greatly change their value with respect to temperature [50].…”