Experiments on Bifurcation of Periodic States into Tori for a Periodically Forced Chemical Oscillator.

摘要

We study experimentally continuous transitions from quasiperiodic states for a time-periodically forced chemical oscillator. The chemical reaction is the hydration of 2,3-epoxy-1-propanol, and is carried out in the autonomous system through supercritical Hopf bifurcations as either the total flow rate or the cooling coil temperature is changed. Under conditions of oscillation for the structure of the toroidal flow, stroboscopic phase portraits, and circle maps as a function of the forcing amplitude and period. A continuous transition from the quasiperiodic to a periodic state, in which the two-torus contracts to a closed curve (Neimark-Sacker torus bifurcation), is observed as the forcing period is changed at a constant moderate forcing amplitude. Qualitative theoretical predictions compare well with the experimental observations. This paper presents the first experimental observation of a Neimark-Sacker torus bifurcation in a forced chemical oscillator system, and relates the bifurcation diagram of the unforced system to that of the forced system reprints. (aw)