Next Article in Journal
Integrating Classical Preprocessing into an Optical Encryption Scheme
Previous Article in Journal
Malevich’s Suprematist Composition Picture for Spin States
Previous Article in Special Issue
Image Encryption Scheme with Compressed Sensing Based on New Three-Dimensional Chaotic System
Open AccessArticle

New Nonlinear Active Element Dedicated to Modeling Chaotic Dynamics with Complex Polynomial Vector Fields

Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 616 00 Brno, Czech Republic
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(9), 871; https://doi.org/10.3390/e21090871
Received: 14 August 2019 / Revised: 1 September 2019 / Accepted: 5 September 2019 / Published: 6 September 2019
This paper describes evolution of new active element that is able to significantly simplify the design process of lumped chaotic oscillator, especially if the concept of analog computer or state space description is adopted. The major advantage of the proposed active device lies in the incorporation of two fundamental mathematical operations into a single five-port voltage-input current-output element: namely, differentiation and multiplication. The developed active device is verified inside three different synthesis scenarios: circuitry realization of a third-order cyclically symmetrical vector field, hyperchaotic system based on the Lorenz equations and fourth- and fifth-order hyperjerk function. Mentioned cases represent complicated vector fields that cannot be implemented without the necessity of utilizing many active elements. The captured oscilloscope screenshots are compared with numerically integrated trajectories to demonstrate good agreement between theory and measurement. View Full-Text
Keywords: bifurcation diagram; chaotic oscillator; Lyapunov exponents; polynomial vector field; squarer; trans-conductance mode bifurcation diagram; chaotic oscillator; Lyapunov exponents; polynomial vector field; squarer; trans-conductance mode
Show Figures

Figure 1

MDPI and ACS Style

Petrzela, J.; Sotner, R. New Nonlinear Active Element Dedicated to Modeling Chaotic Dynamics with Complex Polynomial Vector Fields. Entropy 2019, 21, 871.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map

1
Back to TopTop