649 research outputs found
Synchronization in driven versus autonomous coupled chaotic maps
The phenomenon of synchronization occurring in a locally coupled map lattice
subject to an external drive is compared to the synchronization process in an
autonomous coupled map system with similar local couplings plus a global
interaction. It is shown that chaotic synchronized states in both systems are
equivalent, but the collective states arising after the chaotic synchronized
state becomes unstable can be different in these two systems. It is found that
the external drive induces chaotic synchronization as well as synchronization
of unstable periodic orbits of the local dynamics in the driven lattice. On the
other hand, the addition of a global interaction in the autonomous system
allows for chaotic synchronization that is not possible in a large coupled map
system possessing only local couplings.Comment: 4 pages, 3 figs, accepted in Phys. Rev.
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
Low dimensional behavior in three-dimensional coupled map lattices
The analysis of one-, two-, and three-dimensional coupled map lattices is
here developed under a statistical and dynamical perspective. We show that the
three-dimensional CML exhibits low dimensional behavior with long range
correlation and the power spectrum follows noise. This approach leads to
an integrated understanding of the most important properties of these universal
models of spatiotemporal chaos. We perform a complete time series analysis of
the model and investigate the dependence of the signal properties by change of
dimension.Comment: 7 pages, 6 figures (revised
Error Function Attack of chaos synchronization based encryption schemes
Different chaos synchronization based encryption schemes are reviewed and
compared from the practical point of view. As an efficient cryptanalysis tool
for chaos encryption, a proposal based on the Error Function Attack is
presented systematically and used to evaluate system security. We define a
quantitative measure (Quality Factor) of the effective applicability of a chaos
encryption scheme, which takes into account the security, the encryption speed,
and the robustness against channel noise. A comparison is made of several
encryption schemes and it is found that a scheme based on one-way coupled
chaotic map lattices performs outstandingly well, as judged from Quality
Factor
The identification of complex spatiotemporal patterns using Coupled map lattice model
Many complex and interesting spatiotemporal patterns have been observed in a wide range of scienti¯c areas. In this paper, two kinds of spatiotemporal patterns including spot replication and Turing systems are investigated and new identi¯cation methods are proposed to obtain Coupled Map Lattice (CML) models for this class of systems. Initially, a new correlation analysis method is introduced to determine an appropriate temporal and spatial data sampling step procedure for the identification of spatiotemporal systems. A new combined Orthogonal Forward Regression and Bayesian Learning algorithm with Laplace priors is introduced to identify sparse and robust CML models for complex spatiotemporal patterns. The final identified CML models are validated using correlation based model validation tests for spatiotemporal systems. Numerical re-sults illustrate the identification procedure and demonstrate the validity of the identified models
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