Chaos via duck solution breakdown in a piecewise linear van der Pol oscillator driven by an extremely small periodic perturbation

The response of a circuit which generates the duck solution is studied, where an extremely small periodic perturbation is applied. This perturbation breaks down the duck solution eventually, and then chaos occurs afterwards. To analyze this phenomenon in detail, the piecewise linear technique combined with the degenerate technique is employed. Through this technique, a one-dimensional Poincaré map is derived rigorously, hence chaos generation mechanism is well understood. The bifurcation diagrams are obtained for the circuit, and the parameter boundary between torus generating region and chaos generating region is derived exactly. From these bifurcation diagrams, periodic state breaks down when the forcing term is extremely small.