| Abstract: | In this paper we present
the analytic expressions of partition lines in the parametric space of a piece-wise smooth
mapping describing an electronic relaxation oscillator. The supercritical regions with
permission of period-doubling bifurcation, prohibition of period-doubling bifurcation, and
complete phase-locking are discussed. Among them the region, where period-doubling
bifurcation is prohibited but chaos is permitted is reported for the first time to our
knowledge. These kinds of phenomena and regions can be observed in a lot of similar
systems. |
