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Dec 2012

Volume 22, Issue 4, Articles (04xxxx)

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Chaos 22, 047510 (2012); http://dx.doi.org/10.1063/1.4772195 (33 pages)

Marko Budišić, Ryan Mohr, and Igor Mezić
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Robustness of random graphs based on graph spectra

Jun Wu, Mauricio Barahona, Yue-jin Tan, and Hong-zhong Deng

Chaos 22, 043101 (2012); http://dx.doi.org/10.1063/1.4754875 (7 pages)

Online Publication Date: 4 October 2012

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It has been recently proposed that the robustness of complex networks can be efficiently characterized through the natural connectivity, a spectral property of the graph which corresponds to the average Estrada index. The natural connectivity corresponds to an average eigenvalue calculated from the graph spectrum and can also be interpreted as the Helmholtz free energy of the network. In this article, we explore the use of this index to characterize the robustness of Erdős-Rényi (ER) random graphs, random regular graphs, and regular ring lattices. We show both analytically and numerically that the natural connectivity of ER random graphs increases linearly with the average degree. It is also shown that ER random graphs are more robust than the corresponding random regular graphs with the same number of vertices and edges. However, the relative robustness of ER random graphs and regular ring lattices depends on the average degree and graph size: there is a critical graph size above which regular ring lattices are more robust than random graphs. We use our analytical results to derive this critical graph size as a function of the average degree.
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05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
05.70.Ce Thermodynamic functions and equations of state
05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)
02.10.Ox Combinatorics; graph theory
02.10.Ud Linear algebra
02.60.-x Numerical approximation and analysis

Uncertainty quantification for Markov chain models

Hadi Meidani and Roger Ghanem

Chaos 22, 043102 (2012); http://dx.doi.org/10.1063/1.4757645 (8 pages)

Online Publication Date: 4 October 2012

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Transition probabilities serve to parameterize Markov chains and control their evolution and associated decisions and controls. Uncertainties in these parameters can be associated with inherent fluctuations in the medium through which a chain evolves, or with insufficient data such that the inferential value of the chain is jeopardized. The behavior of Markov chains associated with such uncertainties is described using a probabilistic model for the transition matrices. The principle of maximum entropy is used to characterize the probability measure of the transition rates. The formalism is demonstrated on a Markov chain describing the spread of disease, and a number of quantities of interest, pertaining to different aspects of decision-making, are investigated.
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05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
05.70.Ce Thermodynamic functions and equations of state
02.50.Cw Probability theory
02.50.Ga Markov processes

Shape analysis using fractal dimension: A curvature based approach

André R. Backes, João B. Florindo, and Odemir M. Bruno

Chaos 22, 043103 (2012); http://dx.doi.org/10.1063/1.4757226 (8 pages)

Online Publication Date: 17 October 2012

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The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from a shape by applying a multi-scale approach to the calculus of the fractal dimension. The fractal dimension is estimated by applying the curvature scale-space technique to the original shape. By applying a multi-scale transform to the calculus, we obtain a set of descriptors which is capable of describing the shape under investigation with high precision. We validate the computed descriptors in a classification process. The results demonstrate that the novel technique provides highly reliable descriptors, confirming the efficiency of the proposed method.
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05.45.Df Fractals

Disorder-induced dynamics in a pair of coupled heterogeneous phase oscillator networks

Carlo R. Laing

Chaos 22, 043104 (2012); http://dx.doi.org/10.1063/1.4758814 (9 pages)

Online Publication Date: 17 October 2012

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We consider a pair of coupled heterogeneous phase oscillator networks and investigate their dynamics in the continuum limit as the intrinsic frequencies of the oscillators are made more and more disparate. The Ott/Antonsen Ansatz is used to reduce the system to three ordinary differential equations. We find that most of the interesting dynamics, such as chaotic behaviour, can be understood by analysing a gluing bifurcation of periodic orbits; these orbits can be thought of as “breathing chimeras” in the limit of identical oscillators. We also add Gaussian white noise to the oscillators' dynamics and derive a pair of coupled Fokker-Planck equations describing the dynamics in this case. Comparison with simulations of finite networks of oscillators is used to confirm many of the results.
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05.45.-a Nonlinear dynamics and chaos
02.30.Hq Ordinary differential equations
02.30.Oz Bifurcation theory
02.50.-r Probability theory, stochastic processes, and statistics
05.40.Ca Noise
02.30.-f Function theory, analysis

Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis

Luiz Eduardo Virgilio Silva and Luiz Otavio Murta, Jr.

Chaos 22, 043105 (2012); http://dx.doi.org/10.1063/1.4758815 (7 pages)

Online Publication Date: 17 October 2012

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Complexity in time series is an intriguing feature of living dynamical systems, with potential use for identification of system state. Although various methods have been proposed for measuring physiologic complexity, uncorrelated time series are often assigned high values of complexity, errouneously classifying them as a complex physiological signals. Here, we propose and discuss a method for complex system analysis based on generalized statistical formalism and surrogate time series. Sample entropy (SampEn) was rewritten inspired in Tsallis generalized entropy, as function of q parameter (qSampEn). qSDiff curves were calculated, which consist of differences between original and surrogate series qSampEn. We evaluated qSDiff for 125 real heart rate variability (HRV) dynamics, divided into groups of 70 healthy, 44 congestive heart failure (CHF), and 11 atrial fibrillation (AF) subjects, and for simulated series of stochastic and chaotic process. The evaluations showed that, for nonperiodic signals, qSDiff curves have a maximum point (qSDiffmax) for q ≠ 1. Values of q where the maximum point occurs and where qSDiff is zero were also evaluated. Only qSDiffmax values were capable of distinguish HRV groups (p-values 5.10×10−3, 1.11×10−7, and 5.50×10−7 for healthy vs. CHF, healthy vs. AF, and CHF vs. AF, respectively), consistently with the concept of physiologic complexity, and suggests a potential use for chaotic system analysis.
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87.19.Hh Cardiac dynamics
05.45.Tp Time series analysis
05.45.Ac Low-dimensional chaos
05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
02.50.Fz Stochastic analysis

Robustness to noise in synchronization of network motifs: Experimental results

Arturo Buscarino, Luigi Fortuna, Mattia Frasca, Marco Iachello, and Viet-Thanh Pham

Chaos 22, 043106 (2012); http://dx.doi.org/10.1063/1.4761962 (9 pages)

Online Publication Date: 18 October 2012

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In this work, we experimentally investigate the robustness to noise of synchronization in all the four-nodes network motifs. The experimental setup consists of four Chua's circuits diffusively coupled in order to implement the six different undirected network motifs that can be obtained with four nodes. In this experimental setup, synchronization in the presence of noise injected in one of the network nodes is investigated and network motifs are compared in terms of the synchronization error obtained. The analysis has been then extended to some selected case studies of networks with five and six nodes. Numerical simulations have been also performed and results in agreement with experiments have been obtained. A correlation between node degree and robustness to noise has been found also in these networks.
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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)
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Transmission projective synchronization of multi-systems with non-delayed and delayed coupling via impulsive control

Junwei Sun, Yi Shen, and Guodong Zhang

Chaos 22, 043107 (2012); http://dx.doi.org/10.1063/1.4760251 (10 pages) | Cited 1 time

Online Publication Date: 23 October 2012

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This paper mainly investigates the transmission projective synchronization of multi systems with non-delayed and delayed coupling via impulsive control. Based on the stability analysis of impulsive differential equation, the control laws and updating laws are designed to realize the transmission projective synchronization. Some criteria and corollaries are derived for the transmission projective synchronization among multi-systems. Numerical examples are presented to verify the effectiveness and correctness of the synchronization within a desired scaling factor. For the multi-systems synchronization model, it seems to have more valuable than the usual one drive system and one response system synchronization model.
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05.45.Xt Synchronization; coupled oscillators
02.60.Lj Ordinary and partial differential equations; boundary value problems
02.30.Hq Ordinary differential equations

A novel synchronization scheme with a simple linear control and guaranteed convergence time for generalized Lorenz chaotic systems

Chun-Fu Chuang, Yeong-Jeu Sun, and Wen-June Wang

Chaos 22, 043108 (2012); http://dx.doi.org/10.1063/1.4761818 (7 pages)

Online Publication Date: 23 October 2012

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In this study, exponential finite-time synchronization for generalized Lorenz chaotic systems is investigated. The significant contribution of this paper is that master-slave synchronization is achieved within a pre-specified convergence time and with a simple linear control. The designed linear control consists of two parts: one achieves exponential synchronization, and the other realizes finite-time synchronization within a guaranteed convergence time. Furthermore, the control gain depends on the parameters of the exponential convergence rate, the finite-time convergence rate, the bound of the initial states of the master system, and the system parameter. In addition, the proposed approach can be directly and efficiently applied to secure communication. Finally, four numerical examples are provided to demonstrate the feasibility and correctness of the obtained results.
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05.45.Xt Synchronization; coupled oscillators
02.30.Lt Sequences, series, and summability

Distinguishing similar patterns with different underlying instabilities: Effect of advection on systems with Hopf, Turing-Hopf, and wave instabilities

Igal Berenstein

Chaos 22, 043109 (2012); http://dx.doi.org/10.1063/1.4766591 (4 pages)

Online Publication Date: 13 November 2012

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Systems with the same local dynamics but different types of diffusive instabilities may show the same type of patterns. In this paper, we show that under the influence of advective flow the scenario of patterns that is formed at different velocities change; therefore, we propose the use of advective flow as a tool to uncover the underlying instabilities of a reaction-diffusion system.
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05.60.-k Transport processes
02.30.-f Function theory, analysis
05.45.-a Nonlinear dynamics and chaos

Nonlinear charge transport in the helicoidal DNA molecule

A. Dang Koko, C. B. Tabi, H. P. Ekobena Fouda, A. Mohamadou, and T. C. Kofané

Chaos 22, 043110 (2012); http://dx.doi.org/10.1063/1.4766594 (8 pages)

Online Publication Date: 13 November 2012

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Charge transport in the twist-opening model of DNA is explored via the modulational instability of a plane wave. The dynamics of charge is shown to be governed, in the adiabatic approximation, by a modified discrete nonlinear Schrödinger equation with next-nearest neighbor interactions. The linear stability analysis is performed on the latter and manifestations of the modulational instability are discussed according to the value of the parameter α, which measures hopping interaction correction. In so doing, increasing α leads to a reduction of the instability domain and, therefore, increases our chances of choosing appropriate values of parameters that could give rise to pattern formation in the twist-opening model. Our analytical predictions are verified numerically, where the generic equations for the radial and torsional dynamics are directly integrated. The impact of charge migration on the above degrees of freedom is discussed for different values of α. Soliton-like and localized structures are observed and thus confirm our analytical predictions. We also find that polaronic structures, as known in DNA charge transport, are generated through modulational instability, and hence reinforces the robustness of polaron in the model we study.
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87.15.hj Transport dynamics
87.15.Pc Electronic and electrical properties
87.14.gk DNA
87.15.B- Structure of biomolecules

A “saddle-node” bifurcation scenario for birth or destruction of a Smale–Williams solenoid

Olga B. Isaeva, Sergey P. Kuznetsov, and Igor R. Sataev

Chaos 22, 043111 (2012); http://dx.doi.org/10.1063/1.4766590 (7 pages)

Online Publication Date: 26 November 2012

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Formation or destruction of hyperbolic chaotic attractor under parameter variation is considered with an example represented by Smale–Williams solenoid in stroboscopic Poincaré map of two alternately excited non-autonomous van der Pol oscillators. The transition occupies a narrow but finite parameter interval and progresses in such way that periodic orbits constituting a “skeleton” of the attractor undergo saddle-node bifurcation events involving partner orbits from the attractor and from a non-attracting invariant set, which forms together with its stable manifold a basin boundary of the attractor.
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05.45.Xt Synchronization; coupled oscillators

Ultra-high-frequency piecewise-linear chaos using delayed feedback loops

Seth D. Cohen, Damien Rontani, and Daniel J. Gauthier

Chaos 22, 043112 (2012); http://dx.doi.org/10.1063/1.4766593 (11 pages)

Online Publication Date: 26 November 2012

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We report on an ultra-high-frequency (>1 GHz), piecewise-linear chaotic system designed from low-cost, commercially available electronic components. The system is composed of two electronic time-delayed feedback loops: A primary analog loop with a variable gain that produces multi-mode oscillations centered around 2 GHz and a secondary loop that switches the variable gain between two different values by means of a digital-like signal. We demonstrate experimentally and numerically that such an approach allows for the simultaneous generation of analog and digital chaos, where the digital chaos can be used to partition the system's attractor, forming the foundation for a symbolic dynamics with potential applications in noise-resilient communications and radar.
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05.45.-a Nonlinear dynamics and chaos

Interplay between collective behavior and spreading dynamics on complex networks

Kezan Li, Zhongjun Ma, Zhen Jia, Michael Small, and Xinchu Fu

Chaos 22, 043113 (2012); http://dx.doi.org/10.1063/1.4766677 (10 pages)

Online Publication Date: 26 November 2012

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There are certain correlations between collective behavior and spreading dynamics on some real complex networks. Based on the dynamical characteristics and traditional physical models, we construct several new bidirectional network models of spreading phenomena. By theoretical and numerical analysis of these models, we find that the collective behavior can inhibit spreading behavior, but, conversely, this spreading behavior can accelerate collective behavior. The spread threshold of spreading network is obtained by using the Lyapunov function method. The results show that an effective spreading control method is to enhance the individual awareness to collective behavior. Many real-world complex networks can be thought of in terms of both collective behavior and spreading dynamics and therefore to better understand and control such complex networks systems, our work may provide a basic framework.
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05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)
02.60.-x Numerical approximation and analysis
05.45.-a Nonlinear dynamics and chaos

Effective Fokker-Planck equation for birhythmic modified van der Pol oscillator

R. Yamapi, G. Filatrella, M. A. Aziz-Alaoui, and Hilda A. Cerdeira

Chaos 22, 043114 (2012); http://dx.doi.org/10.1063/1.4766678 (9 pages) | Cited 1 time

Online Publication Date: 26 November 2012

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We present an explicit solution based on the phase-amplitude approximation of the Fokker-Planck equation associated with the Langevin equation of the birhythmic modified van der Pol system. The solution enables us to derive probability distributions analytically as well as the activation energies associated with switching between the coexisting different attractors that characterize the birhythmic system. Comparing analytical and numerical results we find good agreement when the frequencies of both attractors are equal, while the predictions of the analytic estimates deteriorate when the two frequencies depart. Under the effect of noise, the two states that characterize the birhythmic system can merge, inasmuch as the parameter plane of the birhythmic solutions is found to shrink when the noise intensity increases. The solution of the Fokker-Planck equation shows that in the birhythmic region, the two attractors are characterized by very different probabilities of finding the system in such a state. The probability becomes comparable only for a narrow range of the control parameters, thus the two limit cycles have properties in close analogy with the thermodynamic phases.
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05.45.Xt Synchronization; coupled oscillators
02.30.-f Function theory, analysis
02.50.Cw Probability theory

Faster than expected escape for a class of fully chaotic maps

Orestis Georgiou, Carl P. Dettmann, and Eduardo G. Altmann

Chaos 22, 043115 (2012); http://dx.doi.org/10.1063/1.4766723 (10 pages) | Cited 1 time

Online Publication Date: 26 November 2012

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We investigate the dependence of the escape rate on the position of a hole placed in uniformly hyperbolic systems admitting a finite Markov partition. We derive an exact periodic orbit formula for finite size Markov holes which differs from other periodic expansions in the literature and can account for additional distortion to maps with piecewise constant expansion rate. Using asymptotic expansions in powers of hole size we show that for systems conjugate to the binary shift, the average escape rate is always larger than the expectation based on the hole size. Moreover, we show that in the small hole limit the difference between the two decays like a known constant times the square of the hole size. Finally, we relate this problem to the random choice of hole positions and we discuss possible extensions of our results to non-Markov holes as well as applications to leaky dynamical networks.
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05.45.-a Nonlinear dynamics and chaos
02.30.-f Function theory, analysis
02.50.Ga Markov processes
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Emergence of scaling associated with complex branched wave structures in optical medium

Xuan Ni, Ying-Cheng Lai, and Wen-Xu Wang

Chaos 22, 043116 (2012); http://dx.doi.org/10.1063/1.4766757 (11 pages)

Online Publication Date: 26 November 2012

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Branched wave structures, an unconventional wave propagation pattern, can arise in random media. Experimental evidence has accumulated, revealing the occurrence of these waves in systems ranging from microwave and optical systems to solid-state devices. Experiments have also established the universal feature that the wave-intensity statistics deviate from Gaussian and typically possess a long-tail distribution, implying the existence of spatially localized regions with extraordinarily high intensity concentration (“hot” spots). Despite previous efforts, the origin of branched wave pattern is currently an issue of debate. Recently, we proposed a “minimal” model of wave propagation and scattering in optical media, taking into account the essential physics for generating robust branched flows: (1) a finite-size medium for linear wave propagation and (2) random scatterers whose refractive indices deviate continuously from that of the background medium. Here we provide extensive numerical evidence and a comprehensive analytic treatment of the scaling behavior to establish that branched wave patterns can emerge as a general phenomenon in wide parameter regime in between the weak-scattering limit and Anderson localization. The basic physical mechanisms to form branched waves are breakup of waves by a single scatterer and constructive interference of broken waves from multiple scatterers. Despite simplicity of our model, analysis of the scattering field naturally yields an algebraic (power-law) statistic in the high wave-intensity distribution, indicating that our model is able to capture the generic physical origin of these special wave patterns. The insights so obtained can be used to better understand the origin of complex extreme wave patterns, whose occurrences can have significant impact on the performance of the underlying physical systems or devices.
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42.25.Bs Wave propagation, transmission and absorption
42.25.Dd Wave propagation in random media
42.25.Fx Diffraction and scattering
42.25.Hz Interference

The relationship between two fast/slow analysis techniques for bursting oscillations

Wondimu Teka, Joël Tabak, and Richard Bertram

Chaos 22, 043117 (2012); http://dx.doi.org/10.1063/1.4766943 (10 pages) | Cited 1 time

Online Publication Date: 26 November 2012

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Bursting oscillations in excitable systems reflect multi-timescale dynamics. These oscillations have often been studied in mathematical models by splitting the equations into fast and slow subsystems. Typically, one treats the slow variables as parameters of the fast subsystem and studies the bifurcation structure of this subsystem. This has key features such as a z-curve (stationary branch) and a Hopf bifurcation that gives rise to a branch of periodic spiking solutions. In models of bursting in pituitary cells, we have recently used a different approach that focuses on the dynamics of the slow subsystem. Characteristic features of this approach are folded node singularities and a critical manifold. In this article, we investigate the relationships between the key structures of the two analysis techniques. We find that the z-curve and Hopf bifurcation of the two-fast/one-slow decomposition are closely related to the voltage nullcline and folded node singularity of the one-fast/two-slow decomposition, respectively. They become identical in the double singular limit in which voltage is infinitely fast and calcium is infinitely slow.
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02.30.Oz Bifurcation theory

The asymptotic behavior of the order parameter for the infinite-N Kuramoto model

Renato E. Mirollo

Chaos 22, 043118 (2012); http://dx.doi.org/10.1063/1.4766596 (7 pages)

Online Publication Date: 26 November 2012

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The Kuramoto model, first proposed in 1975, consists of a population of sinusoidally coupled oscillators with random natural frequencies. It has served as an idealized model for coupled oscillator systems in physics, chemistry, and biology. This paper addresses a long-standing problem about the infinite-N Kuramoto model, which is to describe the asymptotic behavior of the order parameter for this system. For coupling below a critical level, Kuramoto predicted that the order parameter would decay to 0. We use Fourier transform methods to prove that for general initial conditions, this decay is not exponential; in fact, exponential decay to 0 can only occur if the initial condition satisfies a fairly strong regularity condition that we describe. Our theorem is a partial converse to the recent results of Ott and Antonsen, who proved that for a special class of initial conditions, the order parameter does converge exponentially to its limiting value. Consequently, our result shows that the Ott–Antonsen ansatz does not completely capture all the possible asymptotic behavior in the full Kuramoto system.
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05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.30.Nw Fourier analysis
02.30.Uu Integral transforms
02.50.-r Probability theory, stochastic processes, and statistics

Predicting chaos in memristive oscillator via harmonic balance method

Xin Wang, Chuandong Li, Tingwen Huang, and Shukai Duan

Chaos 22, 043119 (2012); http://dx.doi.org/10.1063/1.4766675 (7 pages)

Online Publication Date: 26 November 2012

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This paper studies the possible chaotic behaviors in a memristive oscillator with cubic nonlinearities via harmonic balance method which is also called the method of describing function. This method was proposed to detect chaos in classical Chua's circuit. We first transform the considered memristive oscillator system into Lur'e model and present the prediction of the existence of chaotic behaviors. To ensure the prediction result is correct, the distortion index is also measured. Numerical simulations are presented to show the effectiveness of theoretical results.
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05.45.Pq Numerical simulations of chaotic systems
02.60.Cb Numerical simulation; solution of equations

Price game and chaos control among three oligarchs with different rationalities in property insurance market

Junhai Ma and Junling Zhang

Chaos 22, 043120 (2012); http://dx.doi.org/10.1063/1.4757225 (13 pages) | Cited 1 time

Online Publication Date: 26 November 2012

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Combining with the actual competition in Chinese property insurance market and assuming that the property insurance companies take the marginal utility maximization as the basis of decision-making when they play price games, we first established the price game model with three oligarchs who have different rationalities. Then, we discussed the existence and stability of equilibrium points. Third, we studied the theoretical value of Lyapunov exponent at Nash equilibrium point and its change process with the main parameters' changes though having numerical simulation for the system such as the bifurcation, chaos attractors, and so on. Finally, we analyzed the influences which the changes of different parameters have on the profits and utilities of oligarchs and their corresponding competition advantage. Based on this, we used the variable feedback control method to control the chaos of the system and stabilized the chaos state to Nash equilibrium point again. The results have significant theoretical and practical application value.
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05.45.Pq Numerical simulations of chaotic systems
89.65.Gh Economics; econophysics, financial markets, business and management
02.30.Yy Control theory
02.50.Le Decision theory and game theory
02.60.Pn Numerical optimization

Reduced dynamics for delayed systems with harmonic or stochastic forcing

Jérémie Lefebvre, Axel Hutt, Victor G. LeBlanc, and André Longtin

Chaos 22, 043121 (2012); http://dx.doi.org/10.1063/1.4760250 (14 pages)

Online Publication Date: 26 November 2012

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The analysis of nonlinear delay-differential equations (DDEs) subjected to external forcing is difficult due to the infinite dimensionality of the space in which they evolve. To simplify the analysis of such systems, the present work develops a non-homogeneous center manifold (CM) reduction scheme, which allows the derivation of a time-dependent order parameter equation in finite dimension. This differential equation captures the major dynamical features of the delayed system. The forcing is assumed to be small compared to the amplitude of the autonomous system, in order to cause only small variations of the fixed points and of the autonomous CM. The time-dependent CM is shown to satisfy a non-homogeneous partial differential equation. We first briefly review CM theory for DDEs. Then we show, for the general scalar case, how an ansatz that separates the CM into one for the autonomous problem plus an additional time-dependent order-two correction leads to satisfying results. The paper then details the application to a transcritical bifurcation subjected to single or multiple periodic forcings. The validity limits of the reduction scheme are also highlighted. Finally, we characterize the specific case of additive stochastic driving of the transcritical bifurcation, where additive white noise shifts the mode of the probability density function of the state variable to larger amplitudes.
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05.40.Ca Noise
02.30.Jr Partial differential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
02.50.Cw Probability theory
02.30.Oz Bifurcation theory

Breaking a chaotic direct sequence spread spectrum communication system using interacting multiple model-unscented Kalman filter

Gan Lu and Xiong Bo

Chaos 22, 043122 (2012); http://dx.doi.org/10.1063/1.4766682 (7 pages)

Online Publication Date: 26 November 2012

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In this paper, a new method to break chaotic direct sequence spread spectrum (CD3S) communication systems is proposed. Here, the CD3S communication system transmitting different information symbols is considered as a combination of two subsystems which are driven by two different chaotic dynamic models, respectively. At every single time moment, the CD3S signal can be regarded as generated by the subsystem corresponding to the information symbol transmitted. Then, based on the multiple model form of CD3S signals, an interacting multiple model unscented Kalman filter with model switching detection mechanism is exploited to track the CD3S signals. The l2-norm of tracking errors is used to choose the model which best matches the intercepted signals. Thus, the information symbols are recovered indirectly. Compared with the existing methods, the proposed algorithm can: (1) reduce the influence of a low spreading factor; (2) calculate the spreading factor using the length of time intervals between model switching; and (3) be more effective under scenarios of low signal-to-noise ratio or multipath fading. Simulation results verify the superiority of the proposed method.
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84.40.Ua Telecommunications: signal transmission and processing; communication satellites

Effect of the heterogeneous neuron and information transmission delay on stochastic resonance of neuronal networks

Qingyun Wang, Honghui Zhang, and Guanrong Chen

Chaos 22, 043123 (2012); http://dx.doi.org/10.1063/1.4767719 (7 pages) | Cited 1 time

Online Publication Date: 26 November 2012

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We study the effect of heterogeneous neuron and information transmission delay on stochastic resonance of scale-free neuronal networks. For this purpose, we introduce the heterogeneity to the specified neuron with the highest degree. It is shown that in the absence of delay, an intermediate noise level can optimally assist spike firings of collective neurons so as to achieve stochastic resonance on scale-free neuronal networks for small and intermediate αh, which plays a heterogeneous role. Maxima of stochastic resonance measure are enhanced as αh increases, which implies that the heterogeneity can improve stochastic resonance. However, as αh is beyond a certain large value, no obvious stochastic resonance can be observed. If the information transmission delay is introduced to neuronal networks, stochastic resonance is dramatically affected. In particular, the tuned information transmission delay can induce multiple stochastic resonance, which can be manifested as well-expressed maximum in the measure for stochastic resonance, appearing every multiple of one half of the subthreshold stimulus period. Furthermore, we can observe that stochastic resonance at odd multiple of one half of the subthreshold stimulus period is subharmonic, as opposed to the case of even multiple of one half of the subthreshold stimulus period. More interestingly, multiple stochastic resonance can also be improved by the suitable heterogeneous neuron. Presented results can provide good insights into the understanding of the heterogeneous neuron and information transmission delay on realistic neuronal networks.
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05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)
02.50.Ey Stochastic processes
05.40.Ca Noise

Effects of weak ties on epidemic predictability on community networks

Panpan Shu, Ming Tang, Kai Gong, and Ying Liu

Chaos 22, 043124 (2012); http://dx.doi.org/10.1063/1.4767955 (8 pages)

Online Publication Date: 26 November 2012

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Weak ties play a significant role in the structures and the dynamics of community networks. Based on the contact process, we study numerically how weak ties influence the predictability of epidemic dynamics. We first investigate the effects of the degree of bridge nodes on the variabilities of both the arrival time and the prevalence of disease, and find out that the bridge node with a small degree can enhance the predictability of epidemic spreading. Once weak ties are settled, the variability of the prevalence will display a complete opposite trend to that of the arrival time, as the distance from the initial seed to the bridge node or the degree of the initial seed increases. More specifically, the further distance and the larger degree of the initial seed can induce the better predictability of the arrival time and the worse predictability of the prevalence. Moreover, we discuss the effects of the number of weak ties on the epidemic variability. As the community strength becomes very strong, which is caused by the decrease of the number of weak ties, the epidemic variability will change dramatically. Compared with the case of the hub seed and the random seed, the bridge seed can result in the worst predictability of the arrival time and the best predictability of the prevalence.
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05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)

Outer synchronization between two complex dynamical networks with discontinuous coupling

Yongzheng Sun, Wang Li, and Donghua Zhao

Chaos 22, 043125 (2012); http://dx.doi.org/10.1063/1.4768661 (8 pages)

Online Publication Date: 29 November 2012

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In this paper, we study the outer synchronization between two complex networks with discontinuous coupling. Sufficient conditions for complete outer synchronization and generalized outer synchronization are obtained based on the stability theory of differential equations. The theoretical results show that two networks can achieve outer synchronization even if two networks are switched off sometimes and the speed of synchronization is proportional to the on-off rate. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results.
Show PACS
05.45.Xt Synchronization; coupled oscillators
02.60.Lj Ordinary and partial differential equations; boundary value problems
05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)
89.75.Hc Networks and genealogical trees
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