RECONSTRUCTING THE DYNAMICS OF UNOBSERVED VARIABLES IN SPATIALLY EXTENDED SYSTEMS

Attractor reconstruction using embedding techniques is a widely used t ool when analysing data from real systems. It allows reconstruction of the system dynamics from only one observable and is thus extremely po werful. We show here that this reconstruction is also possible from sp atially coupled systems. We use a common host-parasitoid model as an e xample as ecological systems are virtually always spatially extended. Additionally, data from ecological systems has often only one observab le, e.g. population density, from a potentially much higher-dimensiona l system. Singular value decomposition is used to show the existence o f a functional relationship mapping the time delayed coordinates of on e variable to the full spatially coupled system. We investigate the ef fects of noise and indicate two important spatial scales. Finally, we illustrate that a reconstruction can be obtained from a system that is only partially sampled.