A New Hyperjerk System With a Half Line Equilibrium: Multistability, Period Doubling Reversals, Antimonotonocity, Electronic Circuit, FPGA Design, and an Application to Image Encryption

Abstract

A hyperjerk system pertains to a dynamical system regulated by an ordinary differential equation of nth order, where n ≥ 4. The main contribution of this work is the finding of a new autonomous hyperjerk system with a half line equilibrium. The mathematical framework of the proposed hyperjerk system contains eight terms with an absolute function nonlinearity. The essential dynamic characteristics of the model are explored, encompassing analysis of equilibrium points and their stability, depiction of the phase trajectories, illustration of bifurcation patterns, and visualization of Lyapunov exponent graphs. Our finding shows that the new 4D hyperjerk system exhibits special behavior like multistability, period doubling reversals and antimonotonocity. The proposed hyperjerk system has been implemented with an electronic circuit using MultiSim 14.0. Moreover, the FPGA implementation of the proposed hyperjerk system is performed by applying two numerical methods: Forward Euler and Trapezoidal. Experimental attractors are given from an oscilloscope by using the Zybo Z7-20 FPGA development board, which are in good agreement with the MATLAB and MultiSim 14.0 simulations. Finally, based on the chaotic dynamical behavior of the proposed chaotic hyperjerk system, a new image encryption approach is proposed. The experimental outcomes of the presented encryption algorithm prove its efficiency and security.

Coherent Chaotic Communication Using Generalized Runge–Kutta Method

“…However, in our study, the noise from quantization is much lower than the noise in the communication channel, and the set of modulation parameters under investigation are sufficient for 12-bit quantization of DAC/ADC and do not affect the quality of message transmission. The use of high-performance platforms such as Raspberry Pi [29,50] and FPGA [51][52][53] with higher-bit resolutions of DAC/ADC can increase the quantitative characteristics of the communication system. However, this work is aimed at assessing the qualitative characteristics and presenting a modulation method that has not previously been described in the scientific literature.…”