Arduino-based Implementation of the Dual-channel Chaotic Generator

Abstract

The paper deals with the development of scientific backgrounds for increasing order of chaotic system and improving its cryptic properties. These backgrounds are based on transforming chaotic systems’ dynamics into multidimensional form by replacing one-dimensional state space variables with multidimensional state vectors. Such transformation can be performed in an easy way for the class of 1-st order nonlinear time-delayed dynamical objects by simple changing state variables. Complex and hypercomplex numbers are used to define both object’s state variables and its parameters. If only state variables are defined with hypercomplex numbers, one can find a chaotic system with several parallel channels without any interrelations between channel. Otherwise, if the object’s parameters are defined with multidimensional vectors, a parallel chaotic system with interrelations between channels can be defined.Since the proposed chaotic generator is implemented on the microcontroller, the transformation of the considered multidimensional chaotic system into discrete form is performed by using backward difference approximation of continuous time derivative operator. Discrete-time model of the multichannel chaotic system makes it possible to define structure, feedforward and feedback parameters of the considered system in an easy way as well as can be implemented on modern microcontrollers. As an example, we consider the Mackey-Glass chaotic system and extend it by using complex numbers. Such an approach allows us to design and implement two channel chaotic system. Since complex numbers are used. one can interpret chaotic oscillations in each channel as multidimensional chaotic oscillations, which are given by their projections or by amplitude and phase.