In this LC oscillator invented by Edwin H. Colpitts in 1927, two capacitors in series along with an inductor, combined with a transistor to provide feedback, sustain the oscillations. This oscillator can show chaotic behavior, which is of interest in applications such as secure communications.
The system of equations describing the Colpitts oscillator can be reduced to
where , , and are parameters that depend on the values of the capacitances and the inductances that determine the frequency of oscillation, as well as on a nonlinear resistance, voltages, and the currents of the transistor.
 H. B. Fotsin and J. Daafouz, "Adaptive Synchronization of Uncertain Chaotic Colpitts Oscillators Based on Parameter Identification," Physics Letters A 339(3–5), 2005 pp. 304–315. doi:10.1016/j.physleta.2005.03.049.