Experimental Observation of Chaotic Attractors from the FPGA implementation of 3D Chaotic Systems

Abstract

In recent years, researchers have designed and implemented chaotic oscillators using digital hardware elements to develop applications like secure communications and random number generation. Due to its programmability and low-cost characteristics, one of the most used digital devices to synthesize chaotic systems is the field-programmable gate array (FPGA), which is recommended for fast prototyping. In this manner, this paper shows the experimental observation of seven chaotic attractors that are simulated using the Verilog hardware description language, and implemented in an FPGA. The seven designs are Lorenz-type systems, which are designed from the discretization of their equations using the well-known Forward Euler method. The block description of the seven chaotic systems employs the fixed-point numerical format using 32 bit. The simulations of the chaotic systems using Matlab and Active-HDL software, along with the block diagrams of the designs, are presented. The final part of the work illustrates the experimental attractors on a Teledyne Lecroy oscilloscope, obtained by using an FPGA Cyclone II EP2C35F672C6 and a 16-bit digital-to-analog converter.