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 Poincare 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.
Highlights
In the last decades, nonlinear systems and especially chaotic systems have aroused tremendous interest because of their applications in many scientific fields, such as in social sciences, ecology, electronic circuits, lasers, chemical reactions, fluid dynamics, mechanical systems, etc. [1, 2], and of many other interesting applications such as in secure communication schemes, cryptography and robotics [3,4,5].At the same period, there has been an exponential use of embedded systems due to the advances in technology, new communication networks and cost-effective solutions
In order to implement the oscillator with hidden attractors into the microprocessor, we use the fourdimensional hyperchaotic Lorenz-type system in discrete mode, using the Euler method [43]
The bifurcation diagram produced by obtained sequential Poincaré maps as the bifurcation parameter (b) decreased with step 0.001
Summary
Nonlinear systems and especially chaotic systems have aroused tremendous interest because of their applications in many scientific fields, such as in social sciences, ecology, electronic circuits, lasers, chemical reactions, fluid dynamics, mechanical systems, etc. [1, 2], and of many other interesting applications such as in secure communication schemes, cryptography and robotics [3,4,5]. There are several embedded applications based on microcontroller such as in military, industry, banking transference, e-commerce, biometric systems, cryptography, robotics, telemedicine, and computing [6], [9,10,11,12,13,14,15,16,17,18]. Literature presents in the last few years some advances of implementing chaotic systems and their applications with a microcontroller. In 2014, the same authors proposed a generalization of four chaotic maps with absolute value nonlinearity [26], which is experimentally implemented by using an Arduino microcontroller. The implementation of a hyperchaotic oscillator with hidden attractors, by using a microcontroller, is proposed.
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