Detect topological horseshoes in the simplest memristor-based chaotic circuit for chaos verification

This paper studies the simplest memristor-based chaotic circuits proposed Muthuswamy and Chua. By defining a two-dimensional Poincaré map, we find a topological horseshoe in the system, reveal the mechanism of the chaotic behavior, and estimate that the topological entropy is not less than 0.5log2, which provides a computer-assisted verification of chaos. Since finding a topological horseshoe is not easy for most researchers, this paper discusses in detail on how to use the Hstool toolbox to do this for the chaotic circuit.