FPGA-Based Numerical Simulation of the Chaotic Synchronization of Chua Circuits

Abstract

The objective of this work was to design and implement a system based on reconfigurable hardware as a study tool for the synchronization of chaotic circuits. Mathematical models were established for one circuit, two synchronized, and multiple synchronized Chua circuits. An ordinary differential equation solver was developed applying Euler’s method using the Verilog hardware description language and synthesized on a Spartan 3E FPGA (Field-Programmable Gate Array) equipped with a 32-bit RISC processor, 64 MB of DDR SDRAM, and 4 Mb of PROM. With a step size of 0.005 and a total of 10,000 iterations, the state equations for one and three Chua circuits were solved at a time of 0.2 ms and a frequency of 50 Mhz. The logical resources used by the system did not exceed 4%. To verify the operation, a numerical simulation was carried out using the Octave V9.1.0 calculation software on an Intel(R) Core i7-9750H CPU 2.59 GHz computer, obtaining the same results but in a time of 493 ms and 3.177 s for one and three circuits, respectively.