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Jun 2012

Volume 22, Issue 2 (partial)

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Components in time-varying graphs

Vincenzo Nicosia, John Tang, Mirco Musolesi, Giovanni Russo, Cecilia Mascolo, and Vito Latora

Chaos 22, 023101 (2012); http://dx.doi.org/10.1063/1.3697996 (11 pages)

Online Publication Date: 5 April 2012

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Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, today it is possible to produce and analyze social and biological networks with detailed information on the time of occurrence and duration of each link. However, standard graph metrics introduced so far in complex network theory are mainly suited for static graphs, i.e., graphs in which the links do not change over time, or graphs built from time-varying systems by aggregating all the links as if they were concurrent in time. In this paper, we extend the notion of connectedness, and the definitions of node and graph components, to the case of time-varying graphs, which are represented as time-ordered sequences of graphs defined over a fixed set of nodes. We show that the problem of finding strongly connected components in a time-varying graph can be mapped into the problem of discovering the maximal-cliques in an opportunely constructed static graph, which we name the affine graph. It is, therefore, an NP-complete problem. As a practical example, we have performed a temporal component analysis of time-varying graphs constructed from three data sets of human interactions. The results show that taking time into account in the definition of graph components allows to capture important features of real systems. In particular, we observe a large variability in the size of node temporal in- and out-components. This is due to intrinsic fluctuations in the activity patterns of individuals, which cannot be detected by static graph analysis.
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05.45.-a Nonlinear dynamics and chaos
89.75.Hc Networks and genealogical trees
02.10.Ox Combinatorics; graph theory
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

A general fractional-order dynamical network: Synchronization behavior and state tuning

Junwei Wang and Xiaohua Xiong

Chaos 22, 023102 (2012); http://dx.doi.org/10.1063/1.3701726 (9 pages)

Online Publication Date: 9 April 2012

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A general fractional-order dynamical network model for synchronization behavior is proposed. Different from previous integer-order dynamical networks, the model is made up of coupled units described by fractional differential equations, where the connections between individual units are nondiffusive and nonlinear. We show that the synchronous behavior of such a network cannot only occur, but also be dramatically different from the behavior of its constituent units. In particular, we find that simple behavior can emerge as synchronized dynamics although the isolated units evolve chaotically. Conversely, individually simple units can display chaotic attractors when the network synchronizes. We also present an easily checked criterion for synchronization depending only on the eigenvalues distribution of a decomposition matrix and the fractional orders. The analytic results are complemented with numerical simulations for two networks whose nodes are governed by fractional-order Lorenz dynamics and fractional-order Rössler dynamics, respectively.
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05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)
02.10.Ud Linear algebra
02.30.Hq Ordinary differential equations
05.45.Xt Synchronization; coupled oscillators

Iterated function system models in data analysis: Detection and separation

Zachary Alexander, James D. Meiss, Elizabeth Bradley, and Joshua Garland

Chaos 22, 023103 (2012); http://dx.doi.org/10.1063/1.3701728 (10 pages)

Online Publication Date: 9 April 2012

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We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete-time dynamical system in which each time step corresponds to the application of one of the finite collection of maps. The maps, which represent distinct dynamical regimes, may be selected deterministically or stochastically. Given a time series from an IFS, our algorithm detects the sequence of regime switches under the assumption that each map is continuous. This method is tested on a simple example and an experimental computer performance data set. This methodology has a wide range of potential uses: from change-point detection in time-series data to the field of digital communications.
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05.45.Tp Time series analysis
02.50.-r Probability theory, stochastic processes, and statistics

Neuronal avalanches of a self-organized neural network with active-neuron-dominant structure

Xiumin Li and Michael Small

Chaos 22, 023104 (2012); http://dx.doi.org/10.1063/1.3701946 (10 pages)

Online Publication Date: 11 April 2012

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Neuronal avalanche is a spontaneous neuronal activity which obeys a power-law distribution of population event sizes with an exponent of –3/2. It has been observed in the superficial layers of cortex both invivo and invitro. In this paper, we analyze the information transmission of a novel self-organized neural network with active-neuron-dominant structure. Neuronal avalanches can be observed in this network with appropriate input intensity. We find that the process of network learning via spike-timing dependent plasticity dramatically increases the complexity of network structure, which is finally self-organized to be active-neuron-dominant connectivity. Both the entropy of activity patterns and the complexity of their resulting post-synaptic inputs are maximized when the network dynamics are propagated as neuronal avalanches. This emergent topology is beneficial for information transmission with high efficiency and also could be responsible for the large information capacity of this network compared with alternative archetypal networks with different neural connectivity.
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87.18.Sn Neural networks and synaptic communication
87.19.lb Action potential propagation and axons
87.19.lj Neuronal network dynamics
87.19.lo Information theory

Experimental evidence of synchronization of time-varying dynamical network

Sourav K. Bhowmick, R. E. Amritkar, and Syamal K. Dana

Chaos 22, 023105 (2012); http://dx.doi.org/10.1063/1.3701949 (9 pages)

Online Publication Date: 12 April 2012

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We investigate synchronization of time varying networks and stability conditions. We derive interesting relations between the critical coupling constants for synchronization and switching times for time-varying and time average networks. The relations are based on the additive property of Lyapunov exponents and are verified experimentally in electronic circuit.
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05.45.Xt Synchronization; coupled oscillators
05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)

Stochastic stability of genetic regulatory networks with a finite set delay characterization

Wenbing Zhang, Yang Tang, Jian-an Fang, and Xiaotai Wu

Chaos 22, 023106 (2012); http://dx.doi.org/10.1063/1.3701994 (12 pages)

Online Publication Date: 12 April 2012

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In this paper, the delay-distribution-dependent stability is derived for the stochastic genetic regulatory networks (GRNs) with a finite set delay characterization and interval parameter uncertainties. One important feature of the obtained results here is that the time-varying delays are assumed to be random and the sum of the occurrence probabilities of the delays is assumed to be 1. By employing a new Lyapunov-Krasovskii functional dependent on auxiliary delay parameters which allow the time-varying delays to be not differentiable, less conservative mean-square stochastic stability criteria are obtained. Finally, two examples are given to illustrate the effectiveness and superiority of the derived results.
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87.16.Yc Regulatory genetic and chemical networks
02.50.Ey Stochastic processes

Using filtering effects to identify objects

T. L. Carroll and Frederic J. Rachford

Chaos 22, 023107 (2012); http://dx.doi.org/10.1063/1.3702566 (9 pages)

Online Publication Date: 12 April 2012

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Reflecting signals off of targets is a method widely used to locate objects, but the reflected signal also contains information that can be used to identify the object. In radar or sonar, the signal amplitudes used are small enough that only linear effects are present, so we can consider the effect of the target on the signal as a linear filter. Using the known effects of linear filters on chaotic signals, we can create a reference that allows us to match a particular target to a particular reflected signal. Furthermore, if some parts of this “filter” vary only slowly as the aspect angle of the object changes, we can produce a reference that averages out the parts that are highly angle dependent so that one reference can be used to identify the target over a range of angles.
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42.30.Sy Pattern recognition
84.40.Ua Telecommunications: signal transmission and processing; communication satellites

Partial synchronization in stochastic dynamical networks with switching communication channels

Chi Huang, Daniel W. C. Ho, Jianquan Lu, and Jürgen Kurths

Chaos 22, 023108 (2012); http://dx.doi.org/10.1063/1.3702576 (12 pages)

Online Publication Date: 13 April 2012

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In this paper, the partial synchronization problem of stochastic dynamical networks (SDNs) is investigated. Unlike the existing models, the SDN considered in this paper suffers from a class of communication constraint—only part of nodes’ states can be transmitted. Thus, less nodes’ states can be used to synchronize the SDN, which makes the analysis of the synchronization problem much harder. A set of channel matrices are introduced to reflect such kind of constraint. Furthermore, due to unpredictable environmental changes, the channel matrices can switch among some communication modes. The switching considered here is governed by a Markov process. To overcome the difficulty, a regrouping method is employed to derive our main results. The obtained conditions guarantee that partial synchronization can be achieved for SDNs under switching communication constraint. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results and how the communication constraint influences synchronization result.
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84.40.Ua Telecommunications: signal transmission and processing; communication satellites
02.10.Yn Matrix theory
02.50.Ey Stochastic processes
02.50.Ga Markov processes

Finite-time stochastic combination synchronization of three different chaotic systems and its application in secure communication

Luo Runzi and Wang Yinglan

Chaos 22, 023109 (2012); http://dx.doi.org/10.1063/1.3702864 (10 pages)

Online Publication Date: 16 April 2012

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In this paper, the finite-time stochastic combination synchronization of three different chaotic systems is investigated. Based on the adaptive technique and the properties of Weiner process, a novel sufficient condition is obtained to ensure combination synchronization under stochastic perturbations. Moreover, a secure communication scheme based on the adaptive combination synchronization of three different systems, i.e., the Lorenz system, Chen system, and Lü system, with uncertainties, unknown parameters, and stochastic perturbation is presented. The simulation results show the feasibility of the proposed method.
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05.45.Xt Synchronization; coupled oscillators
05.45.Mt Quantum chaos; semiclassical methods
03.67.Hk Quantum communication
FREE

Annual variability in a conceptual climate model: Snapshot attractors, hysteresis in extreme events, and climate sensitivity

Tamás Bódai and Tamás Tél

Chaos 22, 023110 (2012); http://dx.doi.org/10.1063/1.3697984 (11 pages)

Online Publication Date: 17 April 2012

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multimedia

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In a conceptual model of global atmospheric circulation, the effects of annually periodic driving are investigated. The driven system is represented in terms of snapshot attractors, which may remain fractal at all times. This is due to the transiently chaotic behavior in the regular parameter regimes of the undriven system. The driving with annual periodicity is found to be relatively fast: There is a considerable deviation from the undriven case. Accordingly, the existence of a hysteresis loop is identified, namely, the extremal values of a given variable depend not only on the actual strength of the insolation but also on the sign of its temporal change. This hysteresis is due to a kind of internal memory. In the threshold-dependence of mean return times of various extreme events, a roughly exponential scaling is found. Climate sensitivity parameters are defined, and the measure of certain types of extremal behavior is found to be strongly susceptible to changes in insolation.
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92.60.Ry Climatology, climate change and variability
92.60.Vb Radiative processes, solar radiation
92.70.Gt Climate dynamics
05.45.Df Fractals

Classical helium atom with radiation reaction

G. Camelio, A. Carati, and L. Galgani

Chaos 22, 023111 (2012); http://dx.doi.org/10.1063/1.4703945 (7 pages)

Online Publication Date: 17 April 2012

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We study a classical model of helium atom in which, in addition to the Coulomb forces, the radiation reaction forces are taken into account. This modification brings in the model a new qualitative feature of a global character. Indeed, as pointed out by Dirac, in any model of classical electrodynamics of point particles involving radiation reaction one has to eliminate, from the a priori conceivable solutions of the problem, those corresponding to the emission of an infinite amount of energy. We show that the Dirac prescription solves a problem of inconsistency plaguing all available models which neglect radiation reaction, namely, the fact that in all such models, most initial data lead to a spontaneous breakdown of the atom. A further modification is that the system thus acquires a peculiar form of dissipation. In particular, this makes attractive an invariant manifold of special physical interest, the zero-dipole manifold that corresponds to motions in which no energy is radiated away (in the dipole approximation). We finally study numerically the invariant measure naturally induced by the time-evolution on such a manifold, and this corresponds to studying the formation process of the atom. Indications are given that such a measure may be singular with respect to that of Lebesgue.
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32.80.Zb Autoionization

Pattern formation in a reaction-diffusion-advection system with wave instability

Igal Berenstein

Chaos 22, 023112 (2012); http://dx.doi.org/10.1063/1.4704809 (4 pages)

Online Publication Date: 19 April 2012

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In this paper, we show by means of numerical simulations how new patterns can emerge in a system with wave instability when a unidirectional advective flow (plug flow) is added to the system. First, we introduce a three variable model with one activator and two inhibitors with similar kinetics to those of the Oregonator model of the Belousov-Zhabotinsky reaction. For this model, we explore the type of patterns that can be obtained without advection, and then explore the effect of different velocities of the advective flow for different patterns. We observe standing waves, and with flow there is a transition from out of phase oscillations between neighboring units to in-phase oscillations with a doubling in frequency. Also mixed and clustered states are generated at higher velocities of the advective flow. There is also a regime of “waving Turing patterns” (quasi-stationary structures that come close and separate periodically), where low advective flow is able to stabilize the stationary Turing pattern. At higher velocities, superposition and interaction of patterns are observed. For both types of patterns, at high velocities of the advective field, the known flow distributed oscillations are observed.
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47.54.Bd Theoretical aspects
02.60.-x Numerical approximation and analysis
47.11.-j Computational methods in fluid dynamics
47.20.-k Flow instabilities
47.35.-i Hydrodynamic waves

Exact folded-band chaotic oscillator

Ned J. Corron and Jonathan N. Blakely

Chaos 22, 023113 (2012); http://dx.doi.org/10.1063/1.4704813 (7 pages)

Online Publication Date: 19 April 2012

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An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler’s oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.
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05.45.-a Nonlinear dynamics and chaos
05.45.Xt Synchronization; coupled oscillators
02.40.Pc General topology

Diffusion in a collisional standard map

M. Rack, K. H. Spatschek, and A. Wingen

Chaos 22, 023114 (2012); http://dx.doi.org/10.1063/1.4704386 (10 pages)

Online Publication Date: 20 April 2012

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Test particle evaluation of the diffusion coefficient in the presence of magnetic field fluctuations and binary collisions is presented. Chaotic magnetic field lines originate from resonant magnetic perturbations (RMPs). To lowest order, charged particles follow magnetic field lines. Drifts and interaction (collisions) with other particles decorrelate particles from the magnetic field lines. We model the binary collision process by a constant collision frequency. The magnetic field configuration including perturbations on the integrable Hamiltonian part is such that the single particle motion can be followed by a collisional version of a Chirikov-Taylor (standard) map. Frequent collisions are allowed for. Scaling of the diffusion beyond the quasilinear and subdiffusive behaviour is investigated in dependence on the strength of the magnetic perturbations and the collision frequency. The appearance of the so called Rechester-Rosenbluth regime is verified. It is further shown that the so called Kadomtsev-Pogutse diffusion coefficient is the strong collisional limit of the Rechester-Rosenbluth formula. The theoretical estimates are supplemented by numerical simulations.
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05.45.Ac Low-dimensional chaos
05.60.-k Transport processes

On finite-size Lyapunov exponents in multiscale systems

Lewis Mitchell and Georg A. Gottwald

Chaos 22, 023115 (2012); http://dx.doi.org/10.1063/1.4704805 (9 pages)

Online Publication Date: 20 April 2012

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We study the effect of regime switches on finite size Lyapunov exponents (FSLEs) in determining the error growth rates and predictability of multiscale systems. We consider a dynamical system involving slow and fast regimes and switches between them. The surprising result is that due to the presence of regimes, the error growth rate can be a non-monotonic function of initial error amplitude. In particular, troughs in the large scales of FSLE spectra are shown to be a signature of slow regimes, whereas fast regimes are shown to cause large peaks in the spectra where error growth rates far exceed those estimated from the maximal Lyapunov exponent. We present analytical results explaining these signatures and corroborate them with numerical simulations. We show further that these peaks disappear in stochastic parametrizations of the fast chaotic processes, and the associated FSLE spectra reveal that large scale predictability properties of the full deterministic model are well approximated, whereas small scale features are not properly resolved.
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05.45.-a Nonlinear dynamics and chaos
02.50.Ey Stochastic processes
02.60.-x Numerical approximation and analysis

Regular and chaotic dynamics of a fountain in a stratified fluid

O. A. Druzhinin and Yu. I. Troitskaya

Chaos 22, 023116 (2012); http://dx.doi.org/10.1063/1.4704814 (14 pages)

Online Publication Date: 20 April 2012

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In the present paper, we study by direct numerical simulation (DNS) and theoretical analysis, the dynamics of a fountain penetrating a pycnocline (a sharp density interface) in a density-stratified fluid. A circular, laminar jet flow of neutral buoyancy is considered, which propagates vertically upwards towards the pycnocline level, penetrates a distance into the layer of lighter fluid, and further stagnates and flows down under gravity around the up-flowing core thus creating a fountain. The DNS results show that if the Froude number (Fr) is small enough, the fountain top remains axisymmetric and steady. However, if Fr is increased, the fountain top becomes unsteady and oscillates in a circular flapping (CF) mode, whereby it retains its shape and moves periodically around the jet central axis. If Fr is increased further, the fountain top rises and collapses chaotically in a bobbing oscillation mode (or B-mode). The development of these two modes is accompanied by the generation of different patterns of internal waves (IW) in the pycnocline. The CF-mode generates spiral internal waves, whereas the B-mode generates IW packets with a complex spatial distribution. The dependence of the amplitude of the fountain-top oscillations on Fr is well described by a Landau-type two-mode-competition model.
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47.52.+j Chaos in fluid dynamics
47.54.Bd Theoretical aspects
47.55.Hd Stratified flows
02.60.Cb Numerical simulation; solution of equations
47.15.Uv Laminar jets
47.35.Bb Gravity waves

“Quorum sensing” generated multistability and chaos in a synthetic genetic oscillator

I. Potapov, B. Zhurov, and E. Volkov

Chaos 22, 023117 (2012); http://dx.doi.org/10.1063/1.4705085 (8 pages)

Online Publication Date: 23 April 2012

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We model the dynamics of the synthetic genetic oscillator Repressilator equipped with quorum sensing. In addition to a circuit of 3 genes repressing each other in a unidirectional manner, the model includes a phase-repulsive type of the coupling module implemented as the production of a small diffusive molecule—autoinducer (AI). We show that the autoinducer (which stimulates the transcription of a target gene) is responsible for the disappearance of the limit cycle (LC) through the infinite period bifurcation and the formation of a stable steady state (SSS) for sufficiently large values of the transcription rate. We found conditions for hysteresis between the limit cycle and the stable steady state. The parameters’ region of the hysteresis is determined by the mRNA to protein lifetime ratio and by the level of transcription-stimulating activity of the AI. In addition to hysteresis, increasing AI-dependent stimulation of transcription may lead to the complex dynamic behavior which is characterized by the appearance of several branches on the bifurcation continuation, containing different regular limit cycles, as well as a chaotic regime. The multistability which is manifested as the coexistence between the stable steady state, limit cycles, and chaos seems to be a novel type of the dynamics for the ring oscillator with the added quorum sensing positive feedback.
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05.45.Xt Synchronization; coupled oscillators
87.15.ap Molecular dynamics simulation
87.14.gk DNA

Generalized complexity measures and chaotic maps

B. Godó and Á. Nagy

Chaos 22, 023118 (2012); http://dx.doi.org/10.1063/1.4705088 (7 pages)

Online Publication Date: 24 April 2012

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The logistic and Tinkerbell maps are studied with the recently introduced generalized complexity measure. The generalized complexity detects periodic windows. Moreover, it recognizes the intersection of periodic branches of the bifurcation diagram. It also reflects the fractal character of the chaotic dynamics. There are cases where the complexity plot shows changes that cannot be seen in the bifurcation diagram.
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05.45.-a Nonlinear dynamics and chaos
05.45.Df Fractals

Alternative interpretations of power-law distributions found in nature

Cécile Penland and Prashant D. Sardeshmukh

Chaos 22, 023119 (2012); http://dx.doi.org/10.1063/1.4706504 (5 pages)

Online Publication Date: 27 April 2012

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We investigate two inherently different classes of probability density functions (pdfs) that share the common property of power law tails: the α-stable Lévy process and the linear Markov diffusion process with additive and multiplicative Gaussian noise. Dynamical processes described by these distributions cannot be uniquely identified as belonging to one or the other class either by diverging variance due to power-law tails in the pdf or by the possible existence of skew. However, there are distinguishing features that may be found in sufficiently well sampled time series. We examine these features and discuss how they may guide the development of proper approximations to equations of motion underlying dynamical systems. An additional result of this research was the identification of a variable describing the relative importance of the multiplicative and independent additive noise forcing in our linear Markov process. The distribution of this variable is generally skewed, depending on the level of correlation between the additive and multiplicative noise.
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05.40.Ca Noise
02.50.Cw Probability theory
02.50.Ga Markov processes
05.45.Tp Time series analysis

Van der Pol and the history of relaxation oscillations: Toward the emergence of a concept

Jean-Marc Ginoux and Christophe Letellier

Chaos 22, 023120 (2012); http://dx.doi.org/10.1063/1.3670008 (15 pages)

Online Publication Date: 30 April 2012

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Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced by self-sustained oscillating systems such as a triode circuit. Our aim is to investigate how relaxation oscillations were actually discovered. Browsing the literature from the late 19th century, we identified four self-oscillating systems in which relaxation oscillations have been observed: (i) the series dynamo machine conducted by Gérard-Lescuyer (1880), (ii) the musical arc discovered by Duddell (1901) and investigated by Blondel (1905), (iii) the triode invented by de Forest (1907), and (iv) the multivibrator elaborated by Abraham and Bloch (1917). The differential equation describing such a self-oscillating system was proposed by Poincaré for the musical arc (1908), by Janet for the series dynamo machine (1919), and by Blondel for the triode (1919). Once Janet (1919) established that these three self-oscillating systems can be described by the same equation, van der Pol proposed (1926) a generic dimensionless equation which captures the relevant dynamical properties shared by these systems. Van der Pol’s contributions during the period of 1926-1930 were investigated to show how, with Le Corbeiller’s help, he popularized the “relaxation oscillations” using the previous experiments as examples and, turned them into a concept.
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84.30.Ng Oscillators, pulse generators, and function generators

Synchronizability of small-world networks generated from ring networks with equal-distance edge additions

Longkun Tang, Jun-an Lu, and Guanrong Chen

Chaos 22, 023121 (2012); http://dx.doi.org/10.1063/1.4711008 (7 pages)

Online Publication Date: 3 May 2012

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This paper investigates the impact of edge-adding number m and edge-adding distance d on both synchronizability and average path length of NW small-world networks generated from ring networks via random edge-adding. It is found that the synchronizability of the network as a function of the distance d is fluctuant and there exist some d that have almost no impact on the synchronizability and may only scarcely shorten the average path length of the network. Numerical simulations on a network of Lorenz oscillators confirm the above results. This phenomenon shows that the contributions of randomly added edges to both the synchronizability and the average path length are not uniform nor monotone in building an NW small-world network with equal-distance edge additions, implying that only if appropriately adding edges when building up the NW small-word network can help enhance the synchronizability and/or reduce the average path length of the resultant network. Finally, it is shown that this NW small-world network has worse synchronizability and longer average path length, when compared with the conventional NW small-world network, with random-distance edge additions. This may be due to the fact that with equal-distance edge additions, there is only one shortcut distance for better information exchange among nodes and for shortening the average path length, while with random-distance edge additions, there exist many different distances for doing so.
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05.45.Xt Synchronization; coupled oscillators
89.75.Hc Networks and genealogical trees
02.50.-r Probability theory, stochastic processes, and statistics
02.60.-x Numerical approximation and analysis
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Fractal structures in two-metal electrodeposition systems II: Cu and Zn

Elias Nakouzi and Rabih Sultan

Chaos 22, 023122 (2012); http://dx.doi.org/10.1063/1.4711007 (7 pages)

Online Publication Date: 7 May 2012

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In this second part of our study on fractal co-electrochemical deposition, we investigate the Cu-Zn system. Macroscopic and microscopic inspection shows a sensitive dependence of the morphology of the final pattern on initial concentrations. The pattern is seen to undergo a transition from classical dendrites to randomly ramified deposits, with each slight increase in [Cu2+]0, while [Zn2+]0 is maintained constant. The variational trends in chemical composition, growth velocity, and fractal dimension with increasing [Cu2+]0 are analyzed. The latter is seen to generally increase with copper (II) ion concentration. In contrast, the growth rate of the deposits is seen to decrease with increasing concentration of Cu2+ ions. A new probe of dense ramified morphology, the pattern density, is introduced and seen to increase with [Cu2+]0. XRD measurements reveal that the observed properties correlate with the birth of copper-rich nuclei, which disrupt the crystalline anisotropy of the two-metal alloy.
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81.15.Pq Electrodeposition, electroplating

Natural time analysis of the Centennial Earthquake Catalog

N. V. Sarlis and S.-R. G. Christopoulos

Chaos 22, 023123 (2012); http://dx.doi.org/10.1063/1.4711374 (7 pages)

Online Publication Date: 9 May 2012

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By using the most recent version (1900–2007) of the Centennial Earthquake Catalog, we examine the properties of the global seismicity. Natural time analysis reveals that the fluctuations of the order parameter κ1 of seismicity exhibit for at least three orders of magnitude a characteristic feature similar to that of the order parameter for other equilibrium or non-equilibrium critical systems—including self-organized critical systems. Moreover, we find non-trivial magnitude correlations for earthquakes of magnitude greater than or equal to 7.
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93.85.Rt Seismic methods
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
05.65.+b Self-organized systems
91.30.Px Earthquakes
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