FPGA Board Implementation of Two Hamiltonian Conservative Chaotic Systems

This work presents, for the first time in the literature, the implementation of two Hamiltonian conservative chaotic systems on an FPGA board, using two different numerical methods to solve the difference equations: the improved Euler and the fourth order Runge-Kutta. The chaotic oscillators that are implemented are two cases of four-dimensional Hamiltonian conservative chaotic systems, which are simulated by MATLAB software obtaining their four different time series. Subsequently, the two cases are digitally implemented on an FPGA board using the MATLAB/Simulink tool in conjunction with the Vivado software for the digital design of the modules in VHDL code. Finally, both the Matlab simulation and the digital emulation are compared, and the FPGA board logical resources used are presented. The original contribution of this work is the design of a digital platform capable of displaying the digital emulation of two cases of Hamiltonian conservative chaotic systems in an analog way, with the flexibility to change their initial conditions and parameters using software.