Electronic Circuit Design, Implementation and FPGA-Based Realization of a New 3D Chaotic System with Single Equilibrium Point

Abstract

In this study, numerical, analog and digital circuit modellings were presented with 3 dimensional, continuous, autonomous new chaotic system. Lyapunov exponentials spectrum and bifurcation diagram were presented with timing series of the new chaotic system, phase portraits and Lyapunov exponentials, equilibrium points, dissipativity analyses. Then, analog-based electronic circuit of the new chaotic system is designed in OrCAD-Pspice. It has been observed that it is a very good match on phase portrait results obtained with the numerical analyses, analog circuit simulation Finally, the new chaotic system presented has been numerically realized in two different models by using Heun and RK4 algorithms with discrete time on FPGA, in order to develop embedded chaos-based engineering applications. In creating Heun and RK4-based two different models of the new chaotic system on FPGA, 32 byte IEEE 754-1985 floating point numerical format was used and coded in VHDL format. Designed chaotic systems were synthesized and tested with Xilinx ISE design tool. Chip statistics obtained from the Place&Route operation in Xilinx Virtex-6 family xc6vlx75t- 3ff784 FPGA chip of the Heun and RK4-based designed chaotic system were presented. Max operation frequency of the new FPGA-based chaotic signal generator modelled by using two different numerical algorithms is determined as 390.067 MHz. Newly presented chotic system’s computer-based numerical simulation was used to realize error analyses fort he design implemented on FPGA. According to the absolute error analysis results, the covergence of 34.456E-5 precision was obtained bwtween the PC-based numerical model and the FPGA-based new chaotic system model.