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.