Method for detecting the signature of noise-induced structures in spatiotemporal data sets.

Spatiotemporal stochastic resonance (STSR) is a phenomenon, where the stability of spatial patterns in an extended dynamical system displays a resonance-type dependence on the noise amplitude with the patterns being optimal at intermediate noise level. This dynamical behavior has been found in theoretical systems as well as in biochemical processes, where the noise level has been controlled externally. However, it is an open question how to identify the signature of a spatiotemporal stochastic resonance in a natural system, e.g., in ecology, when the noise amplitude is not known. This question is addressed in the present paper. We provide analysis tools, which allow to reconstruct the noise intensity in a spatiotemporal data set from the data alone. These tools are based on nearest-neighbor considerations inspired by cellular automata and are an appropriate method for detecting STSR, when combined with some measure of spatial order. As a test of our analysis tools, we apply them to sample data generated by four theoretical model systems. We show explicitly that without knowledge of the theoretical value of the noise amplitude for those systems displaying STSR the corresponding resonance curve can be reconstructed from the data alone. In addition, the other (nonresonant) cases are properly identified by our method with no resonance curve being found.

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.