Analysis of Torus breakdown into Chaos in a Constraint Duffing van der Pol oscillator

The bifurcation structure of a constraint Duffing van der Pol oscillator with a diode is analyzed and an objective bifurcation diagram is illustrated in detail in this work. An idealized case, where the diode is assumed to operate as a switch, is considered.In this case, the Poincaré map is constructed as a one dimensional map: a circle map. The parameter boundary between a torusgenerating region where the circle map is a diffeomorphism and a chaos-generating region where the circle map has extrema is derived explicitly, without solving the implicit equations, by adopting some novel ideas. On the bifurcation diagram, intermittency and a saddle-node bifurcation from the periodic state to the quasi-periodic state can be exactly distinguished. Laboratory experiment is also carried out and theoretical results are verified. keywords: chaos; torus; bifurcation; nonlinear oscillator ∗Electronic address: [email protected] 2