A Novel Simple 4-D Hyperchaotic System with a Saddle-Point Index-2 Equilibrium Point and Multistability: Design and FPGA-Based Applications

Abstract

This paper presents a novel simple 4-D dissipative autonomous hyperchaotic system with a saddle-point index-2 equilibrium point. The dynamics of the new system consists of nine terms with two nonlinear terms. Thus, the proposed system is one of the simplest 4-D hyperchaotic systems. The new system also shows multistability behavior for some range of its parameters. Bifurcation diagrams, Lyapunov spectrum, Kaplan–Yorke dimension, and phase plots are used to analyze the complex dynamical behavior of the system. The discrete-time equivalent of the presented hyperchaotic system is made by using the Euler algorithm for improving the embedded chaos-based engineering applications on FPGA. Then, the design of a novel TRNG having chaotic entropy seed has been performed utilizing FPGA-based 4-D hyperchaotic system structure. The Euler-based model in the creation phase on FPGA has been described using VHDL with 32-bit IEEE 754-1985 floating-point format. The designed hyperchaotic system and TRNG unit have been synthesized using Xilinx ISE Design Tools, and chip statistics obtained from place-and-route process have been presented by testing in the Virtex-6 FPGA chip of Xilinx family. The numbers generated in high data rates of 185.447 Mbit/s have been obtained with 370.894 MHz clock frequency for the implementation of the novel TRNG unit. In the last stage, randomness tests of the generated random numbers have been carried out and the generated random numbers have passed successfully all randomness tests.