44 research outputs found
Inherent global stabilization of unstable local behavior in coupled map lattices
The behavior of two-dimensional coupled map lattices is studied with respect
to the global stabilization of unstable local fixed points without external
control. It is numerically shown under which circumstances such inherent global
stabilization can be achieved for both synchronous and asynchronous updating.
Two necessary conditions for inherent global stabilization are derived
analytically.Comment: 17 pages, 10 figures, accepted for publication in Int.J.Bif.Chao
Stabilization of causally and non-causally coupled map lattices
Two-dimensional coupled map lattices have global stability properties that
depend on the coupling between individual maps and their neighborhood. The
action of the neighborhood on individual maps can be implemented in terms of
"causal" coupling (to spatially distant past states) or "non-causal" coupling
(to spatially distant simultaneous states). In this contribution we show that
globally stable behavior of coupled map lattices is facilitated by causal
coupling, thus indicating a surprising relationship between stability and
causality. The influence of causal versus non-causal coupling for synchronous
and asynchronous updating as a function of coupling strength and for different
neighborhoods is analyzed in detail.Comment: 15 pages, 5 figures, accepted for publication in Physica
Model validation of spatiotemporal systems using correlation function tests
Model validation is an important and essential final step in system identification. Although model validation for nonlinear temporal systems has been extensively studied, model validation for spatiotemporal systems is still an open question. In this paper, correlation based methods, which have been successfully applied in nonlinear temporal systems are extended and enhanced to validate models of spatiotemporal systems. Examples are included to demonstrate the application of the tests
A comparison of polynomial and wavelet expansions for the identification of chaotic coupled map lattices
A comparison between polynomial and wavelet expansions for the identification of coupled map lattice (CML) models for deterministic spatio-temporal dynamical systems is presented in this paper. The pattern dynamics generated by smooth and non-smooth nonlinear maps in a well-known 2-dimensional CML structure are analysed. By using an orthogonal feedforward regression algorithm (OFR), polynomial and wavelet models are identified for the CML’s in chaotic regimes. The quantitative dynamical invariants such as the largest Lyapunov exponents and correlation dimensions are estimated and used to evaluate the performance of the identified models