Rank one chaos in a switch-controlled Chuaʹs circuit

In this paper, we study the existence of strange attractors in a switch-controlled Chuaʹs circuit. This circuit is obtained from the original Chuaʹs circuit by adding externally controlled switches to it in such a way to modulate the system state variables. This investigation is conducted from the perspective of a recent chaos theory of rank one maps. The externally controlled switches are used for the purposes of realizing the general settings of the theory. Both synchronous and asynchronous switch control schemes providing periodic kicks in various directions are investigated, and their effects on the resulting chaotic attractors are discussed. The results of the numerical simulations presented are in close agreement with the expectations of the theory.