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.

Impact factor 1.76

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  • Website
    Chaos website
  • Other titles
    Chaos (Woodbury, N.Y.: Online), Chaos
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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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    • Publisher last contacted on 27/09/2013
  • Classification
    ​ green

Publications in this journal

  • [Show abstract] [Hide abstract]
    ABSTRACT: For an ensemble of globally coupled oscillators with time-delayed interactions, an explicit relation for the frequency of synchronized dynamics corresponding to different phase behaviors is obtained. One class of solutions corresponds to globally synchronized in-phase oscillations. The other class of solutions have mixed phases, and these can be either randomly distributed or can be a splay state, namely with phases distributed uniformly on a circle. In the strong coupling limit and for larger networks, the in-phase synchronized configuration alone remains. Upon variation of the coupling strength or the size of the system, the frequency can change discontinuously, when there is a transition from one class of solutions to another. This can be from the in-phase state to a mixed-phase state, but can also occur between two in-phase configurations of different frequency. Analytical and numerical results are presented for coupled Landau-Stuart oscillators, while numerical results are shown for Rössler and FitzHugh-Nagumo systems.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043111.
  • Chaos (Woodbury, N.Y.) 12/2014; 24(4):040401.
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    ABSTRACT: We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043110.
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    ABSTRACT: In this paper, given a time series generated by a certain dynamical system, we construct a new class of scale-free networks with fractal structure based on the subshift of finite type and base graphs. To simplify our model, we suppose the base graphs are bipartite graphs and the subshift has the special form. When embedding our growing network into the plane, we find its image is a graph-directed self-affine fractal, whose Hausdorff dimension is related to the power law exponent of cumulative degree distribution. It is known that a large spectral gap in terms of normalized Laplacian is usually associated with small mixing time, which makes facilitated synchronization and rapid convergence possible. Through an elaborate analysis of our network, we can estimate its Cheeger constant, which controls the spectral gap by Cheeger inequality. As a result of this estimation, when the bipartite base graph is complete, we give a sharp condition to ensure that our networks are well-connected with rapid mixing property.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043133.
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    ABSTRACT: High-frequency stimulation (HFS) has recently been identified as a novel approach for terminating life-threatening cardiac arrhythmias. HFS elevates myocyte membrane potential and blocks electrical conduction for the duration of the stimulus. However, low amplitude HFS can induce rapidly firing action potentials, which may reinitiate an arrhythmia. The cellular level mechanisms underlying HFS-induced electrical activity are not well understood. Using a multiscale method, we show that a minimal myocyte model qualitatively reproduces the influence of HFS on cardiac electrical activity. Theoretical analysis and simulations suggest that persistent activation and de-inactivation of ionic currents, in particular a fast inward window current, underlie HFS-induced action potentials and membrane potential elevation, providing hypotheses for future experiments. We derive analytical expressions to describe how HFS modifies ionic current amplitude and gating dynamics. We show how fast inward current parameters influence the parameter regimes for HFS-induced electrical activity, demonstrating how the efficacy of HFS as a therapy for terminating arrhythmias may depend on the presence of pathological conditions or pharmacological treatments. Finally, we demonstrate that HFS terminates cardiac arrhythmias in a one-dimensional ring of cardiac tissue. In this study, we demonstrate a novel approach to characterize the influence of HFS on ionic current gating dynamics, provide new insight into HFS of the myocardium, and suggest mechanisms underlying HFS-induced electrical activity.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043104.
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    ABSTRACT: The quantum-classical correspondence is studied for a periodically driven quartic oscillator exhibiting integrable and chaotic dynamics, by studying the Bohmian trajectory of the corresponding "classical" Schrödinger equation. Phase plots and the Kolmogorov-Sinai entropy are computed and compared with the classical trajectory as well as the Bohmian trajectory obtained from the time dependent Schrödinger equation. Bohmian mechanics at the classical limit appears to mimick the behavior of a dissipative dynamical system.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043123.
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    ABSTRACT: In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043108.
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    ABSTRACT: This paper shows the influence of the inner radius on the stability and intensity of vertical vortices, qualitatively similar to dust devils and cyclones, generated in a cylindrical annulus non-homogeneously heated from below. Little relation is found between the intensity of the vortex and the magnitude of the inner radius. Strong stable vortices can be found for both small and large values of the inner radius. The Rankine combined vortex structure, that characterizes the tangential velocity in dust devils, is clearly observed when small values of the inner radius and large values of the ratio between the horizontal and vertical temperature differences are considered. A contraction on the radius of maximum azimuthal velocity is observed when the vortex is intensified by thermal mechanisms. This radius becomes then nearly stationary when frictional force balances the radial inflow generated by the pressure drop in the center, despite the vortex keeps intensifying. These results connect with the behavior of the radius of the maximum tangential wind associated with a hurricane.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043116.
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    ABSTRACT: This paper focuses on the resonance dynamics of a modular neuronal network consisting of several small-world subnetworks. The considered network is composed of delay-coupled FitzHugh-Nagumo (FHN) neurons, whose characteristic parameters present diversity in the form of quenched noise. Our numerical results indicate that when such a network is subjected to an external subthreshold periodic signal, its collective response is optimized for an intermediate level of diversity, namely, a resonant behavior can be induced by an appropriate level of diversity. How the probabilities of intramodule and intermodule connections, as well as the number of subnetworks influence the diversity-induced resonance are also discussed. Further, conclusive evidences demonstrate the nontrivial role of time-delayed coupling on the diversity-induced resonance properties. Especially, multiple resonance is obviously detected when time delays are located at integer multiples of the oscillation period of the signal. Moreover, the phenomenon of fine-tuned delays in inducing multiple resonance remains when diversity is within an intermediate range. Our findings have implications that neural systems may profit from their generic diversity and delayed coupling to optimize the response to external stimulus.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043140.
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    ABSTRACT: This paper introduces two topological models and proposes several topology-based strategies to generate the restoration sequences of the damaged components in a post-disaster power system, and then compares their effectiveness with a random strategy (RS) and a power supply optimized strategy (PSOS, which considers the power flow for restoration optimization), where the strategy effectiveness is quantified by resilience loss defined as the area between real performance curve and target performance curve during the restoration period. Taking the IEEE 300 power system under node failures as an example, results show that under limited restoration resources, topology-based strategies can improve upon the RS-based resilience loss by 39%-46% at most, and their produced average minimum resilience loss is 1.14-1.46 times the PSOS-based resilience loss; when taking restoration sequences generated by topology-based strategies as an input of PSOS, better restoration sequences are found with the resilience loss improved by 16% at most. Similar results are also found under other system parameter settings, other failure types, and other power systems.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043131.
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    ABSTRACT: The Huang method is applied to Seismic Electric Signal (SES) activities in order to decompose them into their components, named Intrinsic Mode Functions (IMFs). We study which of these components contribute to the basic characteristics of the signal. The Hilbert transform is then applied to the IMFs in order to determine their instantaneous amplitudes. The results are compared with those obtained from the analysis in a new time domain termed natural time, after having subtracted the magnetotelluric background from the original signal. It is shown that these instantaneous amplitudes, when combined with the natural time analysis, can be used for the distinction of SES from artificial noises.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043102.
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    ABSTRACT: It has been numerically seen that noise introduces stable well-defined oscillatory state in a system with unstable limit cycles resulting from subcritical Poincaré-Andronov-Hopf (or simply Hopf) bifurcation. This phenomenon is analogous to the well known stochastic resonance in the sense that it effectively converts noise into useful energy. Herein, we clearly explain how noise induced imperfection in the bifurcation is a generic reason for such a phenomenon to occur and provide explicit analytical calculations in order to explain the typical square-root dependence of the oscillations' amplitude on the noise level below a certain threshold value. Also, we argue that the noise can bring forth oscillations in average sense even in the absence of a limit cycle. Thus, we bring forward the inherent general mechanism of the noise induced Hopf bifurcation naturally realisable across disciplines.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043122.
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    ABSTRACT: A financial agent-based price model is developed and investigated by one of statistical physics dynamic systems-the Potts model. Potts model, a generalization of the Ising model to more than two components, is a model of interacting spins on a crystalline lattice which describes the interaction strength among the agents. In this work, we investigate and analyze the correlation behavior of normalized returns of the proposed financial model by the power law classification scheme analysis and the empirical mode decomposition analysis. Moreover, the daily returns of Shanghai Composite Index and Shenzhen Component Index are considered, and the comparison nonlinear analysis of statistical behaviors of returns between the actual data and the simulation data is exhibited.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043113.
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    ABSTRACT: It is explained in which way the ternary symmetric horseshoe can be obtained along a development scenario starting with a binary horseshoe. We explain the case of a complete ternary horseshoe in all detail and then give briefly some further incomplete cases. The key idea is to start with a three degrees of freedom system with a rotational symmetry, reduce the system with the help of the conserved angular momentum to one with two degrees of freedom where the value of the conserved angular momentum acts as a parameter and then let its value go to zero.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043141.
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    ABSTRACT: The non-stationary dynamics of a bouncing ball, comprising both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signatures of self-similarity, complex scaling behavior, and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding to neutral turbulence, viscous dissipation regions, and different time varying periodic modulations.
    Chaos (Woodbury, N.Y.) 12/2014; 24(4):043107.