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Parameter estimation for spatiotemporal dynamics for coupled map lattices and continuous time domain systems is shown using a combination of multiple shooting, Karhunen-Loeve decomposition and Galerkins projection methodologies. The resulting advantages in estimating parameters have been studied and discussed for chaotic and turbulent dynamics using small amounts of data from subsystems, availability of only scalar and noisy time series data, effects of space-time parameter variations, and in the presence of multiple time-scales.
A new type of noise-induced synchronous behavior is described. This phenomenon, called incomplete noise-induced synchronization, arises for one-dimensional Ginzburg-Landau equations driven by common noise. The mechanisms resulting in the incomplete n
The goal of response theory, in each of its many statistical mechanical formulations, is to predict the perturbed response of a system from the knowledge of the unperturbed state and of the applied perturbation. A new recent angle on the problem focu
Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual elements communicate is heterogeneous. Nevertheless, most of pre
We explore the utility of Karhunen Loeve (KL) analysis in solving practical problems in the analysis of gravitational shear surveys. Shear catalogs from large-field weak lensing surveys will be subject to many systematic limitations, notably incomple
Spatially extended systems, such as channel or pipe flows, are often equivariant under continuous symmetry transformations, with each state of the flow having an infinite number of equivalent solutions obtained from it by a translation or a rotation.