Chronobiological analysis of superimposed period data sets using bivariate cosine series models

Abstract

The non-linear cosine fit (so-called cosinor method) of chronobiological sets is suited to one-dimensional effect versus time data. Extending the method to multiple components allows one to look for subharmonics or superimposed underlying periods. In more complex two-dimensional chronobiological time series, alternative models may be advantageous to visualise the time structure. Bivariate cosine series and the corresponding numerical surface discussion including first and second partial derivatives may be a suited method to characterise individual maxima or minima. Moreover, the method permits one to define a mean over two periods (bivariate MESOR) of a two-dimensional data set.