Topological horseshoe analysis on a four-wing chaotic attractor and its FPGA implement

Abstract

For a three-dimensional autonomous four-wing chaotic attractor, this paper rigorously verifies its chaotic properties by using topological horseshoe theory and numerical calculations. Firstly, an appropriate Poincare section of the chaotic attractor is selected by numerical analysis. Accordingly, a certain first return Poincare map is defined in the Poincare section. Thereafter, by utilizing numerical calculations and topological horseshoe theory, a one-dimensional tensile topological horseshoe in the Poincare section is discovered, which revealed that the four-wing attractor has a positive topological entropy, and verifies the existence of chaos in this four-wing attractor. Finally, by using a FPGA chip, the four-wing chaotic attractor was physically implemented, which is more suitable for engineering applications.