A New 8D Lorenz-like Hyperchaotic System: Computer Modelling, Circuit Design and Arduino Uno Board Implementation

Abstract

This paper presents the construction of Matlab-Simulink and LabView models for a novel nonlinear dynamic system of equations in an eight-dimensional (8D) phase space. The Lyapunov exponent spectrum and Kaplan-York dimension were calculated with fixed parameters of the 8D dynamical system. The presence of two positive Lyapunov exponents indicates hyperchaotic behavior. The fractional Kaplan-York dimension shows the fractal structure of strange attractors. An adaptive controller was used to stabilize the 8D chaotic system with unknown system parameters, and an active control method was derived to achieve global chaotic synchronization of two identical 8D chaotic systems with unknown system parameters. Using the results from Matlab-Simulink and LabView models, a chaotic signal generator for the 8D chaotic system was implemented in the Multisim environment. The simulation results of chaotic behavior in the Multisim environment demonstrate similar behavior compared to simulation results from Matlab-Simulink and LabView models. To visualize the new 8D chaotic system, we employed an Arduino Uno board along with eight light-emitting diodes (LEDs). Furthermore, we demonstrated the capability to simulate the new 8D chaotic system in the Proteus 8 environment using the Arduino Uno microcontroller. This advancement in the understanding and implementation of chaotic systems opens doors to numerous possibilities in the realm of secure communication and control systems.