Order and chaos in a third-order RC ladder network with nonlinear feedback

The influence of nonlinear characteristics on the performance of a very simple RC oscillator consisting of a third-order RC -ladder phase-shift network (quadrupole) and a nonlinear amplifier in the feedback path is studied. Proof for the existence of a periodic solution is given, and bounds for the nonlinear characteristic ensuring the existence of a unique periodic solution have been calculated. Bifurcation phenomena associated with the changes of slopes of chosen piecewise-linear characteristics are studied in detail both numerically and experimentally. A complete bifurcation diagram has been constructed revealing several interesting phenomena in the circuit, namely, creation of periodic orbits and symmetry-breaking bifurcation giving birth to two stable periodic orbits, which separately undergo period-doubling bifurcation leading to chaotic behavior. Two coexisting chaotic attractors born via period-doubling sequence finally merge together. Several periodic windows within the chaos range can be detected