RECONSTRUCTION OF SPATIOTEMPORAL SIGNALS OF COMPLEX-SYSTEMS

We propose a novel method to analyze spatio-temporal signals emerging from synergetic systems. By this approach we are able to reconstruct the spatial modes, as well as their dynamic interaction close to instabilities. Our method is an extension of the principal component analysis to the case of nonlinear self-organizing systems. We demonstrate our method by an example of a codimension one instability, apply the algorithm to a simulated Benard instability and present a generalization to bifurcations with several order parameters.