Horseshoes in a class of simple circuits

In this paper we study dynamics of a class of simple single-scroll and two-scrolls type circuits, we show that these circuits are chaotic by giving a rigorous verification for existence of horseshoes in these systems. We prove that the Poincaré map derived from the ordinary differential equations of the single-scroll circuit system is semi-conjugate to the 2-shift map; and the Poincaré map of the two-scrolls circuit system is semi-conjugate to the 4-shift map.