Spatiotemporal chaos control with pinning signals in distributed systems

We suggest a local pinning feedback control for stabilizing periodic pattern in spatially extended systems. Analytical and numerical investigations of this method for a system described by the one-dimensional complex Ginzburg-Landau equation are carried out. We found that it is possible to suppress spatiotemporal chaos by using a few pinning signals in the presence of a large gradient force. Our analytical predictions well coincide with numerical observations.

Transition to Chaos in the Floating Half Zone Convection

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are delta(2) = 4.69 and delta(4) = 4.6, which are comparable with the theoretical asymptotic value delta = 4.669.

Synchronous chaos in the coupled system of two logistic maps

Synchronous chaos is investigated in the coupled system of two Logistic maps. Although the diffusive coupling admits all synchronized motions, the stabilities of their configurations are dependent on the transverse Lyapunov exponents while independent of the longitudinal Lyapunov exponents. It is shown that synchronous chaos is structurally stable with respect to the system parameters. The mean motion is the pseudo-orbit of an individual local map so that its dynamics can be described by the local map. (C) 2004 Elsevier Ltd. All rights reserved.

Chaos of liquid surface waves in a vessel under vertical excitation with slowly modulated amplitude

Free surface waves in a cylinder of liquid under vertical excitation with slowly modulated amplitude are investigated in the current paper. It is shown by both theoretical analysis and numerical simulation that chaos may occur even for a single mode with modulation which can be used to explain Gollub and Meyer's experiment. The implied resonant mechanism accounting for this phenomenon is further elucidated.

Suppressing chaos and transient in parameter perturbed systems

The systems with some system parameters perturbed are investigated. These systems might exist in nature or be obtained by perturbation or truncation theory. Chaos might be suppressed or induced. Some of these dynamical systems exhibit extraordinary long transients, which makes the temporal structure seem sensitively dependent on initial conditions in finite observation time interval.

Convective coupled map for simulating spatiotemporal chaos in flows

A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid hows. It is found that the parameter region of spatiotemporal chaos can be determined by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for turbulence such that the route to spatiotemporal chaos in fluid hows can be envisaged.

Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time-series

We propose here a local exponential divergence plot which is capable of providing an alternative means of characterizing a complex time series. The suggested plot defines a time-dependent exponent and a ''plus'' exponent. Based on their changes with the embedding dimension and delay time, a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time, and the largest Lyapunov exponent has been obtained. When redefining the time-dependent exponent LAMBDA(k) curves on a series of shells, we have found that whether a linear envelope to the LAMBDA(k) curves exists can serve as a direct dynamical method of distinguishing chaos from noise.

Direct dynamical test for deterministic chaos

We present a direct and dynamical method to distinguish low-dimensional deterministic chaos from noise. We define a series of time-dependent curves which are closely related to the largest Lyapunov exponent. For a chaotic time series, there exists an envelope to the time-dependent curves, while for a white noise or a noise with the same power spectrum as that of a chaotic time series, the envelope cannot be defined. When a noise is added to a chaotic time series, the envelope is eventually destroyed with the increasing of the amplitude of the noise.

Molecular phylogenetics of the family Cyprinidae (Actinopterygii : Cypriniformes) as evidenced by sequence variation in the first intron of S7 ribosomal protein-coding gene: Further evidence from a nuclear gene of the systematic chaos in the family

The family Cyprinidae is the largest freshwater fish group in the world, including over 200 genera and 2100 species. The phylogenetic relationships of major clades within this family are simply poorly understood, largely because of the overwhelming diversity of the group; however, several investigators have advanced different hypotheses of relationships that pre- and post-date the use of shared-derived characters as advocated through phylogenetic systematics. As expected, most previous investigations used morphological characters. Recently, mitochondrial DNA (mtDNA) sequences and combined morphological and mtDNA investigations have been used to explore and advance our understanding of species relationships and test monophyletic groupings. Limitations of these studies include limited taxon sampling and a strict reliance upon maternally inherited mtDNA variation. The present study is the first endeavor to recover the phylogenetic relationships of the 12 previously recognized monophyletic subfamilies within the Cyprinidae using newly sequenced nuclear DNA (nDNA) for over 50 species representing members of the different previously hypothesized subfamily and family groupings within the Cyprinidae and from other cypriniform families as outgroup taxa. Hypothesized phylogenetic relationships are constructed using maximum parsimony and Basyesian analyses of 1042 sites, of which 971 sites were variable and 790 were phylogenetically informative. Using other appropriate cypriniform taxa of the families Catostomidae (Myxocyprinus asiaticus), Gyrinocheilidae (Gyrinocheilus aymonieri), and Balitoridae (Nemacheilus sp. and Beaufortia kweichotvensis) as outgroups, the Cyprinidae is resolved as a monophyletic group. Within the family the genera Raiamas, Barilius, Danio, and Rasbora, representing many of the tropical cyprinids, represent basal members of the family. All other species can be classified into variably supported and resolved monophyletic lineages, depending upon analysis, that are consistent with or correspond to Barbini and Leuciscini. The Barbini includes taxa traditionally aligned with the subfamily Cyprininae sensu previous morphological revisionary studies by Howes (Barbinae, Labeoninae, Cyprininae and Schizothoracinae). The Leuciscini includes six other subfamilies that are mainly divided into three separate lineages. The relationships among genera and subfamilies are discussed as well as the possible origins of major lineages. (c) 2008 Published by Elsevier Inc.

Entanglement dynamics and chaos in the Dicke model

We study dynamical properties of quantum entanglement in the Dicke model with and without the rotating-wave approximation. Specifically, we investigate the maximal entanglement and mean entanglement which reflect the underlying chaos in the system, and a good classical-quantum correspondence is found. We also show that the maximal linear entropy can be more sensitive to chaos than the mean linear entropy.

Experimental investigation on the chaotic phenomena in the wake of a natural thermal convection flow

Chaotic phenomena in the wake of thermal convection flow fields above a heating flat plate were investigated experimentally. A newly developed electron beam fluorescence technique (EBF) was used to simultaneously measure density fluctuation at 7 points in a cross section above the plate. Correlation dimensions, intermittence coefficients, Fourier spectrum have been obtained for different Grashof numbers. Spatial distribution of correlation dimensions are presented. The experimental result shows that there is a certain relationship between the density fluctuation and the Gr number. And time-spacial characteristic of chaos evolution is also given.

An improvement and proof of OGY method

OGY method is the most important method of controlling chaos. It stabilizes a hyperbolic periodic orbit by making small perturbations for a system parameter. This paper improves the method of choosing parameter, and gives a mathematics proof of it.

Heteroclinic cycles in lattice dynamical systems

A criterion of spatial chaos occurring in lattice dynamical systems-heteroclinic cycle-is discussed. It is proved that if the system has asymptotically stable heteroclinic cycle, then it has asymptotically stable homoclinic point which implies spatial chaos.

Rotation Numbers Of Invariant Manifolds Around Unstable Periodic Orbits For The Diamagnetic Kepler Problem

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences encoding the periodic orbits in a reduced Poincare section. Only symbolic codes with inverse ordering in the forward mapping can contribute to the rotation of invariant manifolds around the periodic orbits. By using symbolic ordering, the reduced Poincare section is constricted along stable manifolds and a topological template, which preserves the ordering of forward sequences and can be used to extract the rotation numbers, is established. The rotation numbers computed from the topological template are the same as those computed from their original definition.

On properties of hyperchaos: Case study

Some properties of hyperchaos are exploited by studying both uncoupled and coupled CML. In addition to usual properties of chaotic strange attractors, there are other interesting properties, such as: the number of unstable periodic points embedded in the strange attractor increases dramatically increasing and a large number of low-dimensional chaotic invariant sets are contained in the strange attractor. These properties may be useful for regarding the edge of chaos as. the origin of complexity of dynamical systems.