Non periodic oscillations, bistability, coexistence of chaos and hyperchaos in the simplest resistorless Op-Amp based Colpitts oscillator

In the framework of a project on simple circuits with unexpected high degrees of freedom, we report an autonomous microwave oscillator made of a CLC linear resonator of Colpitts type and a single general purpose operational amplifier (Op-Amp). The resonator is in a parallel coupling with the Op-Amp to build the necessary feedback loop of the oscillator. Unlike the general topology of Op-Amp-based oscillators found in the literature including almost always the presence of a negative resistance to justify the nonlinear oscillatory behavior of such circuits, our zero resistor circuit exhibits chaotic and hyperchaotic signals in GHz frequency domain, as well as many other features of complex dynamic systems, including bistability. This simplest form of Colpitts oscillator is adequate to be used as didactic model for the study of complex systems at undergraduate level. Analog and experimental results are proposed.