Period-2 cycles and 2:1 phase locking in a biological clock driven by temperature pulses

Crassulacean acid metabolism (CAM) serves as a botanical model system for the investigation of circadian rhythmicity. In a new set of experiments with the obligatory CAM plant Kalanchoë daigremontiana the response to periodic stimulations with temperature pulses has been studied. On the basis of an experimental phase-response curve of net CO(2)-gas exchange the effect of periodic stimulation has been simulated using a finite-difference equation. These simulations revealed the locations of two period-2 cycles in the CO(2) uptake of the CAM plant. In subsequent experiments based upon the simulated bifurcation diagram the position and amplitude of one of these cycles were confirmed, while experimental evidence for the second cycle could be found. Possible roles of such dynamics for the functioning of the biological clock are discussed.