Chaos (Woodbury, N.Y.) (Chaos )

Publisher: American Institute of Physics; American Institute of Physics. Online Journal Publishing Service, American Institute of Physics


Chaos is a quarterly journal published by the American Institute of Physics and devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.

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  • Website
    Chaos website
  • Other titles
    Chaos (Woodbury, N.Y.: Online), Chaos
  • ISSN
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  • Material type
    Document, Periodical, Internet resource
  • Document type
    Internet Resource, Computer File, Journal / Magazine / Newspaper

Publisher details

American Institute of Physics

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    • NIH-funded articles are automatically deposited with PubMed Central with open access after 12 months
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    • For Medical Physics see AAPM policy
  • Classification
    ​ green

Publications in this journal

  • [Show abstract] [Hide abstract]
    ABSTRACT: We study amplitude-modulated waves, e.g., wave packets in one dimension, overtarget spirals and superspirals in two dimensions, under mixed-mode oscillatory conditions in a three-variable reaction-diffusion model. New transition zones, not seen in the homogeneous system, are found, in which periodic transitions occur between local 1N�1 and 1N oscillations. Amplitude-modulated complex patterns result from periodic transition between (N�1)-armed and N-armed waves. Spatial recurrence rates provide a useful guide to the stability of these modulated patterns. VC 2014 AIP Publishing LLC. []
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023109.
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    ABSTRACT: The motion of beams in particle accelerators is dominated by a plethora of non-linear effects which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2).
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    ABSTRACT: All edges in the classical Watts and Strogatz's small-world network model are unweighted and cooperative (positive). By introducing competitive (negative) inter-cluster edges and assigning edge weights to mimic more realistic networks, this paper develops a modified model which possesses co-competitive weighted couplings and cluster structures while maintaining the common small-world network properties of small average shortest path lengths and large clustering coefficients. Based on theoretical analysis, it is proved that the new model with inter-cluster co-competition balance has an important dynamical property of robust cluster synchronous pattern formation. More precisely, clusters will neither merge nor split regardless of adding or deleting nodes and edges, under the condition of inter-cluster co-competition balance. Numerical simulations demonstrate the robustness of the model against the increase of the coupling strength and several topological variations.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023111.
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    ABSTRACT: We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023112.
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    ABSTRACT: This article proposes an approach to identify fractional-order systems with sparse interaction structures and high dimensions when observation data are supposed to be experimentally available. This approach includes two steps: first, it is to estimate the value of the fractional order by taking into account the solution properties of fractional-order systems; second, it is to identify the interaction coefficients among the system variables by employing the compressed sensing technique. An error analysis is provided analytically for this approach and a further improved approach is also proposed. Moreover, the applicability of the proposed approach is fully illustrated by two examples: one is to estimate the mutual interactions in a complex dynamical network described by fractional-order systems, and the other is to identify a high fractional-order and homogeneous sequential differential equation, which is frequently used to describe viscoelastic phenomena. All the results demonstrate the feasibility of figuring out the system mechanisms behind the data experimentally observed in physical or biological systems with viscoelastic evolution characters.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023119.
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    ABSTRACT: A turbulent flow is usually treated as a superposition of coherent structure and incoherent turbulence. In this paper, the largest Lyapunov exponent and the random noise in the near field of round jet and plane jet are estimated with our previously proposed method of chaotic time series analysis [T. L. Yao, et al., Chaos 22, 033102 (2012)]. The results show that the largest Lyapunov exponents of the round jet and plane jet are in direct proportion to the reciprocal of the integral time scale of turbulence, which is in accordance with the results of the dimensional analysis, and the proportionality coefficients are equal. In addition, the random noise of the round jet and plane jet has the same linear relation with the Kolmogorov velocity scale of turbulence. As a result, the random noise may well be from the incoherent disturbance in turbulence, and the coherent structure in turbulence may well follow the rule of chaotic motion.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023132.
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    ABSTRACT: In the present study, we applied the methodology of the complex network-based time series analysis to experimental temperature time series from a vertical turbulent heated jet. More specifically, we approach the hydrodynamic problem of discriminating time series corresponding to various regions relative to the jet axis, i.e., time series corresponding to regions that are close to the jet axis from time series originating at regions with a different dynamical regime based on the constructed network properties. Applying the transformation phase space method (k nearest neighbors) and also the visibility algorithm, we transformed time series into networks and evaluated the topological properties of the networks such as degree distribution, average path length, diameter, modularity, and clustering coefficient. The results show that the complex network approach allows distinguishing, identifying, and exploring in detail various dynamical regions of the jet flow, and associate it to the corresponding physical behavior. In addition, in order to reject the hypothesis that the studied networks originate from a stochastic process, we generated random network and we compared their statistical properties with that originating from the experimental data. As far as the efficiency of the two methods for network construction is concerned, we conclude that both methodologies lead to network properties that present almost the same qualitative behavior and allow us to reveal the underlying system dynamics.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):024408.
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    ABSTRACT: The dynamics underlying cereal crops in the northern region of Morocco is investigated using a global modelling technique applied to a vegetation index time series derived from satellite measurements, namely, the normalized difference vegetation index from 1982 to 2008. Two three-dimensional chaotic global models of reduced size (14-term and 15-term models) are obtained. The model validation is performed by comparing their horizons of predictability with those provided in previous studies. The attractors produced by the two global models have a complex foliated structure-evidenced in a Poincaré section-rending a topological characterization difficult to perform. Thus, the Kaplan-Yorke dimension is estimated from the synthetic data produced by our global models. Our results suggest that cereal crops in the northern Morocco are governed by a weakly dissipative three-dimensional chaotic dynamics.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023130.
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    ABSTRACT: Liesegang bands are formed when solutions of co-precipitate ions interdiffuse in a 1D gel matrix. In a recent study [R. F. Sultan, Acta. Mech. Sin. 27, 119 (2011)], Liesegang patterns have been characterized as fractal structures. In addition to experimentally obtained patterns, geometric Liesegang patterns were constructed in conformity with the well-known empirical laws. Both mathematical fractal dimensions and box count dimensions for images of PbF2 and PbI2 Liesegang patterns have been calculated. Liesegang patterns can also be described by the entropy state function, and categorized as more or less ordered structures. We revisit the relation between entropy and fractal dimension, and apply it to simulated geometrical Liesegang patterns. We have resort to three different routes for the estimation of the entropy of a Liesegang pattern. The HarFA software enabled the calculation of the Hausdorff dimension and the topological entropy, then the information dimension and the Shannon entropy. In a third pathway, analytical calculations were carried out by estimating the probability of occurrence of a fractal element or coverage. The product of Shannon entropy and Boltzmann constant yields the thermodynamic entropy. The values for PbF2 and PbI2 Liesegang patterns attained the order of magnitude of the reported Third Law entropies, but yet remained lower, in conformity with the more ordered Liesegang structures.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023121.
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    ABSTRACT: Features of the Jacobian matrix of the delay coordinates map are exploited for quantifying the robustness and reliability of state and parameter estimations for a given dynamical model using a measured time series. Relevant concepts of this approach are introduced and illustrated for discrete and continuous time systems employing a filtered Hénon map and a Rössler system.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):024411.
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    ABSTRACT: Square Turing patterns are usually unstable in reaction-diffusion systems and are rarely observed in corresponding experiments and simulations. We report here an example of spontaneous formation of square Turing patterns with the Lengyel-Epstein model of two coupled layers. The squares are found to be a result of the resonance between two supercritical Turing modes with an appropriate ratio. Besides, the spatiotemporal resonance of Turing modes resembles to the mode-locking phenomenon. Analysis of the general amplitude equations for square patterns reveals that the fixed point corresponding to square Turing patterns is stationary when the parameters adopt appropriate values.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023115.
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    ABSTRACT: In the present paper, we study nonlinear dynamics of microtubules (MTs). As an analytical method, we use semi-discrete approximation and show that localized modulated solitonic waves move along MT. This is supported by numerical analysis. Both cases with and without viscosity effects are studied.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023139.
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    ABSTRACT: The human heart normally exhibits robust beat-to-beat heart rate variability (HRV). The loss of this variability is associated with pathology, including disease states such as congestive heart failure (CHF). The effect of general anesthesia on intrinsic HRV is unknown. In this prospective, observational study we enrolled 100 human subjects having elective major surgical procedures under general anesthesia. We recorded continuous heart rate data via continuous electrocardiogram before, during, and after anesthesia, and we assessed HRV of the R-R intervals. We assessed HRV using several common metrics including Detrended Fluctuation Analysis (DFA), Multifractal Analysis, and Multiscale Entropy Analysis. Each of these analyses was done in each of the four clinical phases for each study subject over the course of 24 h: Before anesthesia, during anesthesia, early recovery, and late recovery. On average, we observed a loss of variability on the aforementioned metrics that appeared to correspond to the state of general anesthesia. Following the conclusion of anesthesia, most study subjects appeared to regain their normal HRV, although this did not occur immediately. The resumption of normal HRV was especially delayed on DFA. Qualitatively, the reduction in HRV under anesthesia appears similar to the reduction in HRV observed in CHF. These observations will need to be validated in future studies, and the broader clinical implications of these observations, if any, are unknown.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023129.
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    ABSTRACT: Love stories are dynamic processes that begin, develop, and often stay for a relatively long time in a stationary or fluctuating regime, before possibly fading. Although they are, undoubtedly, the most important dynamic process in our life, they have only recently been cast in the formal frame of dynamical systems theory. In particular, why it is so difficult to predict the evolution of sentimental relationships continues to be largely unexplained. A common reason for this is that love stories reflect the turbulence of the surrounding social environment. But we can also imagine that the interplay of the characters involved contributes to make the story unpredictable-that is, chaotic. In other words, we conjecture that sentimental chaos can have a relevant endogenous origin. To support this intriguing conjecture, we mimic a real and well-documented love story with a mathematical model in which the environment is kept constant, and show that the model is chaotic. The case we analyze is the triangle described in Jules et Jim, an autobiographic novel by Henri-Pierre Roché that became famous worldwide after the success of the homonymous film directed by François Truffaut.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023134.
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    ABSTRACT: The dynamics of the autonomous and non-autonomous Rössler system is studied using the Poincaré recurrence time statistics. It is shown that the probability distribution density of Poincaré recurrences represents a set of equidistant peaks with the distance that is equal to the oscillation period and the envelope obeys an exponential distribution. The dimension of the spatially uniform Rössler attractor is estimated using Poincaré recurrence times. The mean Poincaré recurrence time in the non-autonomous Rössler system is locked by the external frequency, and this enables us to detect the effect of phase-frequency synchronization.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023110.
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    ABSTRACT: By applying Detrended Fluctuation Analysis (DFA) to the time series of the geomagnetic data recorded at three measuring stations in Japan, Rong et al. in 2012 recently reported that anomalous magnetic field variations were identified well before the occurrence of the disastrous Tohoku Mw9.0 earthquake that occurred on 11 March 2011 in Japan exhibiting increased "non-uniform" scaling behavior. Here, we provide an explanation for the appearance of this increase of "non-uniform" scaling on the following grounds: These magnetic field variations are the ones that accompany the electric field variations termed Seismic Electric Signals (SES) activity which have been repeatedly reported that precede major earthquakes. DFA as well as multifractal DFA reveal that the latter electric field variations exhibit scaling behavior as shown by analyzing SES activities observed before major earthquakes in Greece. Hence, when these variations are superimposed on a background of pseudosinusoidal trend, their long range correlation properties-quantified by DFA-are affected resulting in an increase of the "non-uniform" scaling behavior. The same is expected to hold for the former magnetic field variations. This explanation is strengthened by recent findings showing that the fluctuations of the order parameter of seismicity exhibited an unprecedented minimum almost two months before the Tohoku earthquake occurrence which is characteristic for an almost simultaneous emission of Seismic Electric Signals activity.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023131.
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    ABSTRACT: The spreading processes of many infectious diseases have comparable time scale as the network evolution. Here, we present a simple networks model with time-varying community structure, and investigate susceptible-infected-susceptible epidemic spreading processes in this model. By both theoretic analysis and numerical simulations, we show that the efficiency of epidemic spreading in this model depends intensively on the mobility rate q of the individuals among communities. We also find that there exists a mobility rate threshold qc. The epidemic will survive when q > qc and die when q < qc. These results can help understanding the impacts of human travel on the epidemic spreading in complex networks with community structure.
    Chaos (Woodbury, N.Y.) 06/2014; 24(2):023116.

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