Development of nonlinear analysis tools on FPGA

Abstract

Many mathematical models in various scientific fields are represented by complicated differential equations, and such models cannot be solved analytically. Therefore, numerical analysis using computers is essential. However, when a system is more complicated, the analysis time is longer. In this study, we propose a fast numerical analysis method using a field programmable gate array (FPGA). The FPGA is a reconfigurable integrated circuit, and it is good at parallel processing. We developed the calculators of bifurcation diagrams and basins of attraction on an FPGA board. As a result, we constructed calculators that were at most 2.8 times faster and that consumed 95.2% less power than the conventional method using a CPU.