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Top 20 Most Read Articles
January 2012
The 20 articles with the most full-text downloads during the month, in descending order.
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X-ray computerized tomography scan of crumpled aluminum sheet Chaos 19, 041109 (2009); http://dx.doi.org/10.1063/1.3212924 (1 page) Online Publication Date: 27 October 2009
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The impact of awareness on epidemic spreading in networks Chaos 22, 013101 (2012); http://dx.doi.org/10.1063/1.3673573 (8 pages) Online Publication Date: 3 January 2012
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We explore the impact of awareness on epidemic spreading through a population represented by a scale-free network. Using a network mean-field approach, a mathematical model for epidemic spreading with awareness reactions is proposed and analyzed. We focus on the role of three forms of awareness including local, global, and contact awareness. By theoretical analysis and simulation, we show that the global awareness cannot decrease the likelihood of an epidemic outbreak while both the local awareness and the contact awareness can. Also, the influence degree of the local awareness on disease dynamics is closely related with the contact awareness.
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Multiscale dynamics in communities of phase oscillators Chaos 22, 013102 (2012); http://dx.doi.org/10.1063/1.3672513 (12 pages) Online Publication Date: 3 January 2012
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We investigate the dynamics of systems of many coupled phase oscillators with heterogeneous frequencies. We suppose that the oscillators occur in M groups. Each oscillator is connected to other oscillators in its group with “attractive” coupling, such that the coupling promotes synchronization within the group. The coupling between oscillators in different groups is “repulsive,” i.e., their oscillation phases repel. To address this problem, we reduce the governing equations to a lower-dimensional form via the ansatz of Ott and Antonsen, Chaos 18, 037113 (2008). We first consider the symmetric case where all group parameters are the same, and the attractive and repulsive coupling are also the same for each of the M groups. We find a manifold
 of neutrally stable equilibria, and we show that all other equilibria are unstable. For M ≥ 3, has dimension M − 2, and for M = 2, it has dimension 1. To address the general asymmetric case, we then introduce small deviations from symmetry in the group and coupling parameters. Doing a slow/fast timescale analysis, we obtain slow time evolution equations for the motion of the M groups on the manifold . We use these equations to study the dynamics of the groups and compare the results with numerical simulations. |
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Energetics of stochastic resonance Chaos 21, 047516 (2011); http://dx.doi.org/10.1063/1.3658869 (8 pages) Online Publication Date: 29 December 2011
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In this paper, we discuss the motion of a Brownian particle in a double-well potential driven by a periodic force in terms of energies delivered by the periodic and the noise forces and energy dissipated into the viscous environment. It is shown that, while the power delivered by the periodic force to the Brownian particle is controlled by the strength of the noise, the power delivered by the noise itself is independent of the amplitude and frequency of the periodic force. The implications of this result for the mechanism of stochastic resonance in an equilibrium system is that it is not energy from the noise force which enhances a small periodic force, but rather an increase of energy delivered by the periodic force, regulated by the strength of the noise. We further re-evaluate the frequency dependence of stochastic resonance in terms of energetic terms including efficiency.
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Four-dimensional structural dynamics of sheared collagen networks Chaos 21, 041102 (2011); http://dx.doi.org/10.1063/1.3666225 (1 page) Online Publication Date: 20 December 2011
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Chaotic phase synchronization in a modular neuronal network of small-world subnetworks Chaos 21, 043125 (2011); http://dx.doi.org/10.1063/1.3660327 (11 pages) Online Publication Date: 16 November 2011
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We investigate the onset of chaotic phase synchronization of bursting oscillators in a modular neuronal network of small-world subnetworks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that this bursting synchronization transition can be induced not only by the variations of inter- and intra-coupling strengths but also by changing the probability of random links between different subnetworks. We also analyze the effect of external chaotic phase synchronization of bursting behavior in this clustered network by an external time-periodic signal applied to a single neuron. Simulation results demonstrate a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this synchronization region increases with the signal amplitude and the number of driven neurons but decreases rapidly with the network size. Considering that the synchronization of bursting neurons is thought to play a key role in some pathological conditions, the presented results could have important implications for the role of externally applied driving signal in controlling bursting activity in neuronal ensembles.
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Introduction to Focus Issue: Nonlinear and Stochastic Physics in Biology Chaos 21, 047501 (2011); http://dx.doi.org/10.1063/1.3671647 (6 pages) Online Publication Date: 29 December 2011
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Frank Moss was a leading figure in the study of nonlinear and stochastic processes in biological systems. His work, particularly in the area of stochastic resonance, has been highly influential to the interdisciplinary scientific community. This Focus Issue pays tribute to Moss with articles that describe the most recent advances in the field he helped to create. In this Introduction, we review Moss’s seminal scientific contributions and introduce the articles that make up this Focus Issue.
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Chaos 21, 037101 (2011); http://dx.doi.org/10.1063/1.3643065 (5 pages) Online Publication Date: 30 September 2011
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We introduce the contributions to this Focus Issue and describe their origin in a recent Santa Fe Institute workshop.
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Transcripts: An algebraic approach to coupled time series Chaos 22, 013105 (2012); http://dx.doi.org/10.1063/1.3673238 (13 pages) Online Publication Date: 13 January 2012
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Ordinal symbolic dynamics is based on ordinal patterns. Its tools include permutation entropy (in metric and topological versions), forbidden patterns, and a number of mathematical results that make this sort of symbolic dynamics appealing both for theoreticians and practitioners. In particular, ordinal symbolic dynamics is robust against observational noise and can be implemented with low computational cost, which explains its increasing popularity in time series analysis. In this paper, we study the perhaps less exploited aspect so far of ordinal patterns: their algebraic structure. In a first part, we revisit the concept of transcript between two symbolic representations, generalize it to N representations, and derive some general properties. In a second part, we use transcripts to define two complexity indicators of coupled dynamics. Their performance is tested with numerical and real world data.
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Resonance phenomena and long-term chaotic advection in volume-preserving systems Chaos 22, 013103 (2012); http://dx.doi.org/10.1063/1.3672510 (8 pages) Online Publication Date: 3 January 2012
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Creating chaotic advection is the most efficient strategy to achieve mixing on microscale or in very viscous fluids. In this paper, we present a quantitative theory of the long-time resonant mixing in 3D near-integrable flows. We use the flow between two coaxial elliptic counter-rotating cylinders as a demonstrative model, where multiple scatterings on resonance result in mixing by causing the jumps of adiabatic invariants. We improve the existing estimates of the width of the mixing domain. We show that the resulting mixing both on short and long time scales can be described in terms of a single diffusion-type equation with a diffusion coefficient depending on the averaged effect of multiple passages through resonances. We discuss the exact location of the boundaries of the chaotic domain and show how it affects the properties of mixing.
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Introduction: Eighth Annual Gallery of Nonlinear Images (Dallas, Texas, 2011) Chaos 21, 041101 (2011); http://dx.doi.org/10.1063/1.3671937 (1 page) Online Publication Date: 20 December 2011
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Chaos 21, 047522 (2011); http://dx.doi.org/10.1063/1.3629984 (6 pages) Online Publication Date: 29 December 2011
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This paper focuses on a paced genetic regulatory small-world network with time-delayed coupling. How the dynamical behaviors including temporal resonance and spatial synchronization evolve under the influence of time-delay and connection topology is explored through numerical simulations. We reveal the phenomenon of delay-induced resonance when the network topology is fixed. For a fixed time-delay, temporal resonance is shown to be degraded by increasing the rewiring probability of the network. On the other hand, for small rewiring probability, temporal resonance can be enhanced by an appropriately tuned small delay but degraded by a large delay, while conversely, temporal resonance is always reduced by time-delay for large rewiring probability. Finally, an optimal spatial synchrony is detected by a proper combination of time-delay and connection topology.
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Detecting the topologies of complex networks with stochastic perturbations Chaos 21, 043129 (2011); http://dx.doi.org/10.1063/1.3664396 (9 pages) Online Publication Date: 2 December 2011
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How to recover the underlying connection topology of a complex network from observed time series of a component variable of each node subject to random perturbations is studied. A new technique termed Piecewise Granger Causality is proposed. The validity of the new approach is illustrated with two FitzHugh-Nagumo neurobiological networks by only observing the membrane potential of each neuron, where the neurons are coupled linearly and nonlinearly, respectively. Comparison with the traditional Granger causality test is performed, and it is found that the new approach outperforms the traditional one. The impact of the network coupling strength and the noise intensity, as well as the data length of each partition of the time series, is further analyzed in detail. Finally, an application to a network composed of coupled chaotic Rössler systems is provided for further validation of the new method.
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How granular materials jam in a hopper Chaos 21, 041107 (2011); http://dx.doi.org/10.1063/1.3669495 (1 page) Online Publication Date: 20 December 2011
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A common repressor pool results in indeterminacy of extrinsic noise Chaos 21, 047523 (2011); http://dx.doi.org/10.1063/1.3658618 (12 pages) Online Publication Date: 29 December 2011
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For just over a decade, stochastic gene expression has been the focus of many experimental and theoretical studies. It is now widely accepted that noise in gene expression can be decomposed into extrinsic and intrinsic components, which have orthogonal contributions to the total noise. Intrinsic noise stems from the random occurrence of biochemical reactions and is inherent to gene expression. Extrinsic noise originates from fluctuations in the concentrations of regulatory components or random transitions in the cell’s state and is imposed to the gene of interest by the intra- and extra-cellular environment. The basic assumption has been that extrinsic noise acts as a pure input on the gene of interest, which exerts no feedback on the extrinsic noise source. Thus, multiple copies of a gene would be uniformly influenced by an extrinsic noise source. Here, we report that this assumption falls short when multiple genes share a common pool of a regulatory molecule. Due to the competitive utilization of the molecules existing in this pool, genes are no longer uniformly influenced by the extrinsic noise source. Rather, they exert negative regulation on each other and thus extrinsic noise cannot be determined by the currently established method.
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Sensory coding in oscillatory electroreceptors of paddlefish Chaos 21, 047505 (2011); http://dx.doi.org/10.1063/1.3669494 (14 pages) Online Publication Date: 29 December 2011
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Coherence and information theoretic analyses were applied to quantitate the response properties and the encoding of time-varying stimuli in paddlefish electroreceptors (ERs), studied in vivo. External electrical stimuli were Gaussian noise waveforms of varied frequency band and strength, including naturalistic waveforms derived from zooplankton prey. Our coherence analyses elucidated the role of internal oscillations and transduction processes in shaping the 0.5–20 Hz best frequency tuning of these electroreceptors, to match the electrical signals emitted by zooplankton prey. Stimulus-response coherence fell off above approximately 20 Hz, apparently due to intrinsic limits of transduction, but was detectable up to 40–50 Hz. Aligned with this upper fall off was a narrow band of intense internal noise at ∼25 Hz, due to prominent membrane potential oscillations in cells of sensory epithelia, which caused a narrow deadband of external insensitivity. Using coherence analysis, we showed that more than 76% of naturalistic stimuli of weak strength, ∼1 μV/cm, was linearly encoded into an afferent spike train, which transmitted information at a rate of ∼30 bits/s. Stimulus transfer to afferent spike timing became essentially nonlinear as the stimulus strength was increased to induce bursting firing. Strong stimuli, as from nearby zooplankton prey, acted to synchronize the bursting responses of afferents, including across populations of electroreceptors, providing a plausible mechanism for reliable information transfer to higher-order neurons through noisy synapses.
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Variability of spatio-temporal patterns in non-homogeneous rings of spiking neurons Chaos 21, 047511 (2011); http://dx.doi.org/10.1063/1.3665200 (11 pages) Online Publication Date: 29 December 2011
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We show that a ring of unidirectionally delay-coupled spiking neurons may possess a multitude of stable spiking patterns and provide a constructive algorithm for generating a desired spiking pattern. More specifically, for a given time-periodic pattern, in which each neuron fires once within the pattern period at a predefined time moment, we provide the coupling delays and/or coupling strengths leading to this particular pattern. The considered homogeneous networks demonstrate a great multistability of various travelling time- and space-periodic waves which can propagate either along the direction of coupling or in opposite direction. Such a multistability significantly enhances the variability of possible spatio-temporal patterns and potentially increases the coding capability of oscillatory neuronal loops. We illustrate our results using FitzHugh-Nagumo neurons interacting via excitatory chemical synapses as well as limit-cycle oscillators.
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Brownian motors and stochastic resonance Chaos 21, 047503 (2011); http://dx.doi.org/10.1063/1.3661160 (6 pages) Online Publication Date: 29 December 2011
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We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.
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Chaos 21, 047521 (2011); http://dx.doi.org/10.1063/1.3660159 (8 pages) Online Publication Date: 29 December 2011
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Following the advent of synthetic biology, several gene networks have been engineered to emulate digital devices, with the ability to program cells for different applications. In this work, we adapt the concept of logical stochastic resonance to a synthetic gene network derived from a bacteriophage λ. The intriguing results of this study show that it is possible to build a biological logic block that can emulate or switch from the AND to the OR gate functionalities through externally tuning the system parameters. Moreover, this behavior and the robustness of the logic gate are underpinned by the presence of an optimal amount of random fluctuations. We extend our earlier work in this field, by taking into account the effects of correlated external (additive) and internal (multiplicative or state-dependent) noise. Results obtained through analytical calculations as well as numerical simulations are presented.
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Huygens (and others) revisited Chaos 21, 047515 (2011); http://dx.doi.org/10.1063/1.3665201 (10 pages) Online Publication Date: 29 December 2011
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We develop a generic iterative map model of coupled oscillators based on simple physical processes common to many such systems. The model allows us to understand, from a unified perspective, the range of different outcomes reported for experiments by Huygens and modern realizations of his two coupled clocks.
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