Synchronization and control of spatiotemporal chaos using time-series data from local regions

Abstract

In this paper we show that the analysis of the dynamics in localized regions, i.e., sub-systems can be used to characterize the chaotic dynamics and the synchronization ability of the spatiotemporal systems. Using noisy scalar time-series data for driving along with simultaneous self-adaptation of the control parameter representative control goals like suppressing spatiotemporal chaos and synchronization of spatiotemporally chaotic dynamics have been discussed. (c) 1998 American Institute of Physics.

Estimation of intensive quantities in spatio-temporal systems from time-series

“…These quantities were first estimated from experimental data in [29]. Extensive studies have shown that for spatially extended systems, and in particular for coupled map lattices, the so-called sub-system LS converges rapidly towards the LS of the whole system for increasing sub-system size [18][19][20][21]. Instead of using all the N variables of the system to build the Jacobian we only take a subset N s of these variables (from N s neighbouring sites) and build the Jacobian for this N s -dimensional sub-system without changing the underlying dynamics for the whole original system.…”

“…This relies on the rescaling property of the Lyapunov spectrum: it has been observed that for many systems exhibiting spatio-temporal chaos, the spectrum of a sub-system, when suitably rescaled, can give a good approximation of the spectrum of the whole spatio-temporal system [18][19][20][21]. Once the Lyapunov spectrum has been computed, other related quantities such as the Lyapunov dimension density and Kolmogorov-Sinai (KS) entropy density can also be determined.…”

Embedded multiple shooting methodology in a genetic algorithm framework for parameter estimation and state identification of complex systems

“…Studies show that for a sub-system model of the process that considers only the equations for the variables not being monitored (i.e., X 1 ; X 2 Þ, the dynamics of these sub-model variables (i.e.,X 1 ;X 2 Þ will synchronize completely with those of the process, if the conditional Lyapunov exponents of the sub-model are all negative (Pecora and Carroll, 1990;Parekh et al, 1998;Pikovsky et al, 2003). Simulation studies evaluating the conditional Lyapunov exponents for A-B-C reaction in the CSTR have in fact shown the negativity of the corresponding conditional exponents.…”

Quasidiagonal approach to the estimation of Lyapunov spectra for spatiotemporal systems from multivariate time series

“…D L and h increase linearly with N ). Moreover, it is useful to introduce their respective densities by simply dividing them by the system volume (lattice size) [25]. This even allows such quantities to be defined in the thermodynamic limit, although care has to be taken in doing this for systems such as PDEs where space is continuous [26].…”