Rigorous analysis of Arnold tongues in a manifold piecewise-linear circuit

In nonlinear systems which exhibit oscillation phenomena, it is well-known that phase-locked regions (also called as Arnold tongues) are often observed. However, the examples of theoretical analysis of Arnold tongues and bifurcation phenomena in autonomous circuit are quite rare. Therefore, in this paper, we propose an autonomous manifold piecewise-linear circuit. The Poincare map of this circuit is a explicit equation and thus can be rigorously derived. Using the Poincare map, we consider the generation and rigorous analysis some interesting nonlinear phenomena such as quasi-periodic oscillation, Arnold tongues and bifurcation phenomena.