A New 6D Chaotic Generator: Computer Modelling and Circuit Design

Abstract

The objective of this study aims at using the Matlab-Simulink environment and the LabVIEW software environment to build computer models of a six-dimensional (6D) chaotic dynamic system. For the fixed system’s parameters, the spectrum of Lyapunov exponents and the Kaplan-York dimension are calculated. The presence of two positive Lyapunov exponents demonstrates the hyperchaotic behavior of the system. The fractional Kaplan-York dimension indicates the fractal structure of strange attractors. An active control method is extended to achieve global chaotic synchronization of two identical novel 6D chaotic systems with unknown system parameters. Based on the results obtained in Matlab-Simulink and LabVIEW models, a chaotic signal generator for the 6D chaotic system is implemented in the MultiSim environment. The experimental results show that the chaotic behavior simulation in the MultiSim environment is similar to those in the Matlab-Simulink and LabVIEW models. The simulation results demonstrate that the Pecora-Carroll method is a simple way of chaotic masking and signal decoding.

Dynamical analysis, circuit design, synchronization, and Arduino UNO implementation of a new 7D hyperchaotic system

“…Recently, in [25], we conducted a computer simulation of a 6D chaotic system, outlining scenarios for the emergence of a turbulent state in a non-uniformly rotating magnetized electrically conducting fluid. The model is characterized by nonlinear dynamic equations of the following form [25]:…”

Analysis, circuit design, and synchronization of a new 8D memristor-based chaotic system with application to chaotic masking and signal decoding

“…This section introduces a novel multidimensional chaotic system incorporating a memristor, achieved through the fusion of the "memristor" element with the 6D chaotic system equations of the following form 25 :…”

“…These diagrams furnish important insights into the qualitative shifts in the system's behavior as specific control parameters undergo variations. Following a methodology akin to that in reference 25 , we designate the parameter R in the system (6) as a controlling factor. The bifurcation diagrams aid in identifying stable regions or regular behaviors within the system, represented by individual points.…”

“…Figure 8 illustrates the block diagram of an 8D hyperchaotic memristor-based system, described by transformed equations (10). Unlike previous works 25 , 32 , this model was created using the Control & Simulation and Formula Node toolkits. The Formula Node is employed to articulate the right-hand sides of the equations in the system (10).…”

“…This study introduces a novel 8D hyperchaotic system, representing an extension of the six-dimensional equations in nonlinear dynamics. Specifically, it addresses magnetic convection in a nonuniformly rotating electrically conductive fluid, as outlined in the paper 25 . In an effort to enhance chaos, the equations governing the 6D nonlinear dynamics were enriched with a "memristor," resulting in the derivation of a new eight-dimensional (8D) nonlinear system of equations.…”