The Colpitts oscillator: Families of periodic solutions and their bifurcations

In this work we consider the Colpitts oscillator as a paradigm for sinusoidal oscillation and we investigate its nonlinear dynamics. In particular, we carry out a two-parameter bifurcation analysis of a model of the oscillator. This analysis is conducted by combining numerical continuation techniques and normal form theory. First, we show that the birth of the harmonic cycle is associated with a Hopf bifurcation and we discuss the effects of idealization in the model. Various families of limit cycles are identified and their bifurcations are analyzed in detail. In particular, we demonstrate that the bifurcation diagram in the parameter space is organized by an infinite family of homoclinic bifurcations. Finally, local and global coexistence phenomena are described.