The Colpitts oscillator: Families of periodic solutions and their bifurcations

In this work we consider the Colpitts oscillator as a paradigm for sinusoid al oscillation and we investigate its nonlinear dynamics. In particular, we carry out a two-parameter bifurcation analysis of a model of the oscillato r. This analysis is conducted by combining numerical continuation technique s and normal form theory. First, we show that the birth of the harmonic cyc le is associated with a Hopf bifurcation and we discuss the effects of idea lization in the model. Various families of limit cycles are identified and their bifurcations are analyzed in detail. In particular, we demonstrate th at the bifurcation diagram in the parameter space is organized by an infini te family of homoclinic bifurcations. Finally, local and global coexistence phenomena are described.