Detecting nonlinear dynamics in spatio-temporal systems, examples from ecological models

Mathematical models of marine populations exhibit chaotic dynamics. However, we hypothesize that in moving water, Eulerian sampling of spatially heterogeneous populations may obscure any deterministic signal beyond the resolving capabilities of presently available nonlinear signal processing techniques. To examine this hypothesis we created two spatio-temporal models of population dynamics. To caricature actual ocean sampling limitations, we sampled the model output in two ways, random walks to simulate Eulerian sampling, and spatial averages to simulate population measurements from finite volumes. Results indicate that the ability to identify underlying nonlinear dynamics quickly degrades as the step size of a random walk sampling increases. On the other hand, the analysis techniques used are more robust in the face of spatial averaging.