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Sep 2011

Volume 21, Issue 3, Articles (03xxxx)

Issue Cover Spotlight Figure

Chaos 21, 037101 (2011); http://dx.doi.org/10.1063/1.3643065 (5 pages)

James P. Crutchfield and Jon Machta

Cover image is adapted from Fig. 16 of John R. Mahoney, Christopher J. Ellison, Ryan G. James, and James P. Crutchfield, Chaos 21, 037112 (2011), Figs. 8 and 9 of Ryan G. James, Christopher J. Ellison, and James P. Crutchfield, Chaos 21, 037109 (2011), and Fig. 4 of Benjamin Flecker, Wesley Alford, John M. Beggs, Paul L. Williams, and Randall D. Beer, Chaos 21, 037104 (2011). The cover image is a collage of various information diagrams, each of which illustrates the set-theoretic relationships between different kinds of information determined from process information measures and from the partial information decomposition. Collage by James Crutchfield (Complexity Sciences Center, Physics Department, University of California, Davis).

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First numerical investigation of a conjecture by N. N. Nekhoroshev about stability in quasi-integrable systems

Massimiliano Guzzo, Elena Lega, and Claude Froeschlé

Chaos 21, 033101 (2011); http://dx.doi.org/10.1063/1.3603819 (12 pages)

Online Publication Date: 19 July 2011

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We investigate numerically a conjecture by N. N. Nekhoroshev about the influence of a geometric property, called steepness, on the long term stability of quasi-integrable systems. In a Nekhoroshev’s 1977 paper, it is conjectured that, among the steep systems with the same number ν of frequencies, the convex ones are the most stable, and it is suggested to investigate numerically the problem. Following this suggestion, we numerically study and compare the diffusion of the actions in quasi-integrable systems with different steepness properties in a large range of variation of the perturbation parameter ɛ and different dimensions of phase space corresponding to ν = 3 and ν = 4 (ν ≤ 2 is not significant for the conjecture). For six dimensional maps (ν = 4), our numerical experiments perfectly agree with the Nekhoroshev conjecture: for both convex and non convex cases, the numerically computed diffusion coefficient D of the actions is compatible with an exponential fit, and the convex case is definitely more stable than the steep one. For four dimensional maps (ν = 3), since we find that in the steep case D(ɛ) has large oscillations around an exponential behaviour, the agreement of our numerical experiments with the conjecture is not sharp, and it is found by considering a sup over different initial conditions.
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02.60.Jh Numerical differentiation and integration
05.60.-k Transport processes

How to combine independent data sets for the same quantity

Theodore P. Hill and Jack Miller

Chaos 21, 033102 (2011); http://dx.doi.org/10.1063/1.3593373 (8 pages)

Online Publication Date: 20 July 2011

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This paper describes a new mathematical method called conflation for consolidating data from independent experiments that measure the same physical quantity. Conflation is easy to calculate and visualize and minimizes the maximum loss in Shannon information in consolidating several independent distributions into a single distribution. A formal mathematical treatment of conflation has recently been published. For the benefit of experimenters wishing to use this technique, in this paper we derive the principal basic properties of conflation in the special case of normally distributed (Gaussian) data. Examples of applications to measurements of the fundamental physical constants and in high energy physics are presented, and the conflation operation is generalized to weighted conflation for cases in which the underlying experiments are not uniformly reliable.
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05.45.Gg Control of chaos, applications of chaos
06.20.Jr Determination of fundamental constants

Complex networks analysis of obstructive nephropathy data

M. Zanin and S. Boccaletti

Chaos 21, 033103 (2011); http://dx.doi.org/10.1063/1.3608126 (5 pages)

Online Publication Date: 22 July 2011

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Congenital obstructive nephropathy (ON) is one of the most frequent and complex diseases affecting children, characterized by an abnormal flux of the urine, due to a partial or complete obstruction of the urinary tract; as a consequence, urine may accumulate in the kidney and disturb the normal operation of the organ. Despite important advances, pathological mechanisms are not yet fully understood. In this contribution, the topology of complex networks, based on vectors of features of control and ON subjects, is related with the severity of the pathology. Nodes in these networks represent genetic and metabolic profiles, while connections between them indicate an abnormal relation between their expressions. Resulting topologies allow discriminating ON subjects and detecting which genetic or metabolic elements are responsible for the malfunction.
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89.75.Hc Networks and genealogical trees
87.19.xk Genetic diseases
87.15.K- Molecular interactions; membrane-protein interactions
87.18.Cf Genetic switches and networks
87.19.xt Developmental diseases

Synchronization based system identification of an extended excitable system

S. Berg, S. Luther, and U. Parlitz

Chaos 21, 033104 (2011); http://dx.doi.org/10.1063/1.3613921 (6 pages)

Online Publication Date: 25 July 2011

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A basic state and parameter estimation scheme for an extended excitable system is presented, where time series from a spatial grid of sampling points are used to drive and synchronize corresponding model equations. Model parameters are estimated by minimizing the synchronization error. This estimation scheme is demonstrated using data from generic models of excitable media exhibiting spiral wave dynamics and chaotic spiral break-up that are implemented on a graphics processing unit.
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05.45.-a Nonlinear dynamics and chaos
05.45.Xt Synchronization; coupled oscillators
02.30.Jr Partial differential equations

Lyapunov exponent diagrams of a 4-dimensional Chua system

Cristiane Stegemann, Holokx A. Albuquerque, Rero M. Rubinger, and Paulo C. Rech

Chaos 21, 033105 (2011); http://dx.doi.org/10.1063/1.3615232 (7 pages) | Cited 1 time

Online Publication Date: 25 July 2011

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We report numerical results on the existence of periodic structures embedded in chaotic and hyperchaotic regions on the Lyapunov exponent diagrams of a 4-dimensional Chua system. The model was obtained from the 3-dimensional Chua system by the introduction of a feedback controller. Both the largest and the second largest Lyapunov exponents were considered in our colorful Lyapunov exponent diagrams, and allowed us to characterize periodic structures and regions of chaos and hyperchaos. The shrimp-shaped periodic structures appear to be malformed on some of Lyapunov exponent diagrams, and they present two different bifurcation scenarios to chaos when passing the boundaries of itself, namely via period-doubling and crisis. Hyperchaos-chaos transition can also be observed on the Lyapunov exponent diagrams for the second largest exponent.
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05.45.Pq Numerical simulations of chaotic systems
05.45.Ac Low-dimensional chaos
02.30.Yy Control theory
02.60.-x Numerical approximation and analysis

Novel vibrational resonance in multistable systems

S. Rajasekar, K. Abirami, and M. A. F. Sanjuan

Chaos 21, 033106 (2011); http://dx.doi.org/10.1063/1.3610213 (7 pages) | Cited 2 times

Online Publication Date: 29 July 2011

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We investigate the role of multistable states on the occurrence of vibrational resonance in a periodic potential system driven by both a low-frequency and a high-frequency periodic force in both underdamped and overdamped limits. In both cases, when the amplitude of the high-frequency force is varied, the response amplitude at the low-frequency exhibits a series of resonance peaks and approaches a limiting value. Using a theoretical approach, we analyse the mechanism of multiresonance in terms of the resonant frequency and the stability of the equilibrium points of the equation of motion of the slow variable. In the overdamped system, the response amplitude is always higher than in the absence of the high-frequency force. However, in the underdamped system, this happens only if the low-frequency is less than 1. In the underdamped system, the response amplitude is maximum when the equilibrium point around which slow oscillations take place is maximally stable and minimum at the transcritical bifurcation. And in the overdamped system, it is maximum at the transcritical bifurcation and minimum when the associated equilibrium point is maximally stable. When the periodicity of the potential is truncated, the system displays only a few resonance peaks.
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46.40.Ff Resonance, damping, and dynamic stability
43.40.-r Structural acoustics and vibration
45.05.+x General theory of classical mechanics of discrete systems

On decomposing mixed-mode oscillations and their return maps

Christian Kuehn

Chaos 21, 033107 (2011); http://dx.doi.org/10.1063/1.3615231 (15 pages)

Online Publication Date: 29 July 2011

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Alternating patterns of small and large amplitude oscillations occur in a wide variety of physical, chemical, biological, and engineering systems. These mixed-mode oscillations (MMOs) are often found in systems with multiple time scales. Previous differential equation modeling and analysis of MMOs have mainly focused on local mechanisms to explain the small oscillations. Numerical continuation studies reported different MMO patterns based on parameter variation. This paper aims at improving the link between local analysis and numerical simulation. Our starting point is a numerical study of a singular return map for the Koper model which is a prototypical example for MMOs, which also relates to local normal form theory. We demonstrate that many MMO patterns can be understood geometrically by approximating the singular maps with affine and quadratic maps. Motivated by our numerical analysis we use abstract affine and quadratic return map models in combination with two local normal forms that generate small oscillations. Using this decomposition approach we can reproduce many classical MMO patterns and effectively decouple bifurcation parameters for local and global parts of the flow. The overall strategy we employ provides an alternative technique for understanding MMOs.
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05.45.-a Nonlinear dynamics and chaos
02.30.Hq Ordinary differential equations

A phase-synchronization and random-matrix based approach to multichannel time-series analysis with application to epilepsy

Ivan Osorio and Ying-Cheng Lai

Chaos 21, 033108 (2011); http://dx.doi.org/10.1063/1.3615642 (11 pages)

Online Publication Date: 1 August 2011

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We present a general method to analyze multichannel time series that are becoming increasingly common in many areas of science and engineering. Of particular interest is the degree of synchrony among various channels, motivated by the recognition that characterization of synchrony in a system consisting of many interacting components can provide insights into its fundamental dynamics. Often such a system is complex, high-dimensional, nonlinear, nonstationary, and noisy, rendering unlikely complete synchronization in which the dynamical variables from individual components approach each other asymptotically. Nonetheless, a weaker type of synchrony that lasts for a finite amount of time, namely, phase synchronization, can be expected. Our idea is to calculate the average phase-synchronization times from all available pairs of channels and then to construct a matrix. Due to nonlinearity and stochasticity, the matrix is effectively random. Moreover, since the diagonal elements of the matrix can be arbitrarily large, the matrix can be singular. To overcome this difficulty, we develop a random-matrix based criterion for proper choosing of the diagonal matrix elements. Monitoring of the eigenvalues and the determinant provides a powerful way to assess changes in synchrony. The method is tested using a prototype nonstationary noisy dynamical system, electroencephalogram (scalp) data from absence seizures for which enhanced cortico-thalamic synchrony is presumed, and electrocorticogram (intracranial) data from subjects having partial seizures with secondary generalization for which enhanced local synchrony is similarly presumed.
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87.19.lm Synchronization in the nervous system
87.19.le EEG and MEG
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Stability, bifurcations, and dynamics of global variables of a system of bursting neurons

Igor Franović, Kristina Todorović, Nebojša Vasović, and Nikola Burić

Chaos 21, 033109 (2011); http://dx.doi.org/10.1063/1.3619293 (9 pages)

Online Publication Date: 5 August 2011

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An approximate mean field model of an ensemble of delayed coupled stochastic Hindmarsh-Rose bursting neurons is constructed and analyzed. Bifurcation analysis of the approximate system is performed using numerical continuation. It is demonstrated that the stability domains in the parameter space of the large exact systems are correctly estimated using the much simpler approximate model.
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05.45.-a Nonlinear dynamics and chaos

Stability of strategies in payoff-driven evolutionary games on networks

Francesco Sorrentino and Nicholas Mecholsky

Chaos 21, 033110 (2011); http://dx.doi.org/10.1063/1.3613924 (10 pages)

Online Publication Date: 9 August 2011

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We consider a network of coupled agents playing the Prisoner’s Dilemma game, in which players are allowed to pick a strategy in the interval [0, 1], with 0 corresponding to defection, 1 to cooperation, and intermediate values representing mixed strategies in which each player may act as a cooperator or a defector over a large number of interactions with a certain probability. Our model is payoff-driven, i.e., we assume that the level of accumulated payoff at each node is a relevant parameter in the selection of strategies. Also, we consider that each player chooses his/her strategy in a context of limited information. We present a deterministic nonlinear model for the evolution of strategies. We show that the final strategies depend on the network structure and on the choice of the parameters of the game. We find that polarized strategies (pure cooperator/defector states) typically emerge when (i) the network connections are sparse, (ii) the network degree distribution is heterogeneous, (iii) the network is assortative, and surprisingly, (iv) the benefit of cooperation is high.
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89.75.Hc Networks and genealogical trees
02.50.Cw Probability theory
02.50.Le Decision theory and game theory

Adaptive mechanism between dynamical synchronization and epidemic behavior on complex networks

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

Chaos 21, 033111 (2011); http://dx.doi.org/10.1063/1.3622678 (6 pages) | Cited 1 time

Online Publication Date: 12 August 2011

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Many realistic epidemic networks display statistically synchronous behavior which we will refer to as epidemic synchronization. However, to the best of our knowledge, there has been no theoretical study of epidemic synchronization. In fact, in many cases, synchronization and epidemic behavior can arise simultaneously and interplay adaptively. In this paper, we first construct mathematical models of epidemic synchronization, based on traditional dynamical models on complex networks, by applying the adaptive mechanisms observed in real networks. Then, we study the relationship between the epidemic rate and synchronization stability of these models and, in particular, obtain the conditions of local and global stability for epidemic synchronization. Finally, we perform numerical analysis to verify our theoretical results. This work is the first to draw a theoretical bridge between epidemic transmission and synchronization dynamics and will be beneficial to the study of control and the analysis of the epidemics on complex networks.
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89.75.Hc Networks and genealogical trees
02.60.-x Numerical approximation and analysis
05.45.Xt Synchronization; coupled oscillators

Cascading failures and the emergence of cooperation in evolutionary-game based models of social and economical networks

Wen-Xu Wang, Ying-Cheng Lai, and Dieter Armbruster

Chaos 21, 033112 (2011); http://dx.doi.org/10.1063/1.3621719 (12 pages)

Online Publication Date: 17 August 2011

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We study catastrophic behaviors in large networked systems in the paradigm of evolutionary games by incorporating a realistic “death” or “bankruptcy” mechanism. We find that a cascading bankruptcy process can arise when defection strategies exist and individuals are vulnerable to deficit. Strikingly, we observe that, after the catastrophic cascading process terminates, cooperators are the sole survivors, regardless of the game types and of the connection patterns among individuals as determined by the topology of the underlying network. It is necessary that individuals cooperate with each other to survive the catastrophic failures. Cooperation thus becomes the optimal strategy and absolutely outperforms defection in the game evolution with respect to the “death” mechanism. Our results can be useful for understanding large-scale catastrophe in real-world systems and in particular, they may yield insights into significant social and economical phenomena such as large-scale failures of financial institutions and corporations during an economic recession.
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89.75.Hc Networks and genealogical trees
89.65.Gh Economics; econophysics, financial markets, business and management
05.45.-a Nonlinear dynamics and chaos
02.40.Re Algebraic topology

Nonlinear vocal fold dynamics resulting from asymmetric fluid loading on a two-mass model of speech

Byron D. Erath, Matías Zañartu, Sean D. Peterson, and Michael W. Plesniak

Chaos 21, 033113 (2011); http://dx.doi.org/10.1063/1.3615726 (8 pages)

Online Publication Date: 22 August 2011

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Nonlinear vocal fold dynamics arising from asymmetric flow formations within the glottis are investigated using a two-mass model of speech with asymmetric vocal fold tensioning, representative of unilateral vocal fold paralysis. A refined theoretical boundary-layer flow solver is implemented to compute the intraglottal pressures, providing a more realistic description of the flow than the standard one-dimensional, inviscid Bernoulli flow solution. Vocal fold dynamics are investigated for subglottal pressures of 0.6 < ps < 1.5 kPa and tension asymmetries of 0.5 < Q < 0.8. As tension asymmetries become pronounced the asymmetric flow incites nonlinear behavior in the vocal fold dynamics at subglottal pressures that are associated with normal speech, behavior that is not captured with standard Bernoulli flow solvers. Regions of bifurcation, coexistence of solutions, and chaos are identified.
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43.72.-p Speech processing and communication systems
43.25.-x Nonlinear acoustics
43.28.-g Aeroacoustics and atmospheric sound
47.11.-j Computational methods in fluid dynamics

Generating and enhancing lag synchronization of chaotic systems by white noise

Zhongkui Sun and Xiaoli Yang

Chaos 21, 033114 (2011); http://dx.doi.org/10.1063/1.3623440 (10 pages)

Online Publication Date: 23 August 2011

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In this paper, we study the crucial impact of white noise on lag synchronous regime in a pair of time-delay unidirectionally coupled systems. Our result demonstrates that merely via white-noise-based coupling lag synchronization could be achieved between the coupled systems (chaotic or not). And it is also demonstrated that a conventional lag synchronous regime can be enhanced by white noise. Sufficient conditions are further proved mathematically for noise-inducing and noise-enhancing lag synchronization, respectively. Additionally, the influence of parameter mismatch on the proposed lag synchronous regime is studied, by which we announce the robustness and validity of the new strategy. Two numerical examples are provided to illustrate the validity and some possible applications of the theoretical result.
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05.45.Xt Synchronization; coupled oscillators
02.60.-x Numerical approximation and analysis
05.40.Ca Noise

Stability and chaotification of vibration isolation floating raft systems with time-delayed feedback control

Y. L. Li, D. L. Xu, Y. M. Fu, and J. X. Zhou

Chaos 21, 033115 (2011); http://dx.doi.org/10.1063/1.3615710 (10 pages)

Online Publication Date: 25 August 2011

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This paper presents a systematic study on the stability of a two-dimensional vibration isolation floating raft system with a time-delayed feedback control. Based on the generalized Sturm criterion, the critical control gain for the delay-independent stability region and critical time delays for the stability switches are derived. The critical conditions can provide a theoretical guidance of chaotification design for line spectra reduction. Numerical simulations verify the correctness of the approach. Bifurcation analyses reveal that chaotification is more likely to occur in unstable region defined by these critical conditions, and the stiffness of the floating raft and mass ratio are the sensitive parameters to reduce critical control gain.
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89.20.Kk Engineering
43.40.-r Structural acoustics and vibration
45.80.+r Control of mechanical systems

Transient chaos in optical metamaterials

Xuan Ni and Ying-Cheng Lai

Chaos 21, 033116 (2011); http://dx.doi.org/10.1063/1.3623436 (7 pages)

Online Publication Date: 26 August 2011

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We investigate the dynamics of light rays in two classes of optical metamaterial systems: (1) time-dependent system with a volcano-shaped, inhomogeneous and isotropic refractive-index distribution, subject to external electromagnetic perturbations and (2) time-independent system consisting of three overlapping or non-overlapping refractive-index distributions. Utilizing a mechanical-optical analogy and coordinate transformation, the wave-propagation problem governed by the Maxwell’s equations can be modeled by a set of ordinary differential equations for light rays. We find that transient chaotic dynamics, hyperbolic or nonhyperbolic, are common in optical metamaterial systems. Due to the analogy between light-ray dynamics in metamaterials and the motion of light in matter as described by general relativity, our results reinforce the recent idea that chaos in gravitational systems can be observed and studied in laboratory experiments.
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05.45.-a Nonlinear dynamics and chaos
42.25.Bs Wave propagation, transmission and absorption
42.70.Nq Other nonlinear optical materials; photorefractive and semiconductor materials
02.30.Hq Ordinary differential equations
03.50.De Classical electromagnetism, Maxwell equations
04.20.Jb Exact solutions

Flights in a pseudo-chaotic system

J. H. Lowenstein and F. Vivaldi

Chaos 21, 033117 (2011); http://dx.doi.org/10.1063/1.3624797 (15 pages)

Online Publication Date: 30 August 2011

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We consider the problem of transport in a one-parameter family of piecewise rotations of the torus, for rotation number approaching 1/4. This is a zero-entropy system which in this limit exhibits a divided phase space, with island chains immersed in a “pseudo-chaotic” region. We identify a novel mechanism for long-range transport, namely the adiabatic destruction of accelerator-mode islands. This process originates from the approximate translational invariance of the phase space and leads to long flights of linear motion, for a significant measure of initial conditions. We show that the asymptotic probability distribution of the flight lengths is determined by the geometric properties of a partition of the accelerator-mode island associated with the flight. We establish the existence of flights travelling distances of order O(1) in phase space. We provide evidence for the existence of a scattering process that connects flights travelling in opposite directions.
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05.45.-a Nonlinear dynamics and chaos
05.60.-k Transport processes
05.70.Ce Thermodynamic functions and equations of state
02.50.Cw Probability theory

Synchronization in counter-rotating oscillators

Sourav K. Bhowmick, Dibakar Ghosh, and Syamal K. Dana

Chaos 21, 033118 (2011); http://dx.doi.org/10.1063/1.3624943 (9 pages)

Online Publication Date: 1 September 2011

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An oscillatory system can have opposite senses of rotation, clockwise or anticlockwise. We present a general mathematical description of how to obtain counter-rotating oscillators from the definition of a dynamical system. A type of mixed synchronization emerges in counter-rotating oscillators under diffusive scalar coupling when complete synchronization and antisynchronization coexist in different state variables. We present numerical examples of limit cycle van der Pol oscillator and chaotic Rössler and Lorenz systems. Stability conditions of mixed synchronization are analytically obtained for both Rössler and Lorenz systems. Experimental evidences of counter-rotating limit cycle and chaotic oscillators and mixed synchronization are given in electronic circuits.
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05.45.Xt Synchronization; coupled oscillators

Pinning control of complex networks via edge snapping

P. DeLellis, M. di Bernardo, and M. Porfiri

Chaos 21, 033119 (2011); http://dx.doi.org/10.1063/1.3626024 (13 pages)

Online Publication Date: 6 September 2011

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In this paper, we propose a hierarchy of novel decentralized adaptive pinning strategies for controlled synchronization of complex networks. This hierarchy addresses the fundamental need of selecting the sites to pin through a fully decentralized approach based on edge snapping. Specifically, we present three different strategies of increasing complexity which use a combination of network evolution and adaptation of the coupling and control gains. Theoretical results are complemented by extensive numerical investigations of the performance of the proposed strategies on a set of testbed examples.
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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)
02.30.Hq Ordinary differential equations
02.30.Yy Control theory
02.60.Lj Ordinary and partial differential equations; boundary value problems

Chaotic solitons in the quadratic-cubic nonlinear Schrödinger equation under nonlinearity management

J. Fujioka, E. Cortés, R. Pérez-Pascual, R. F. Rodríguez, A. Espinosa, and B. A. Malomed

Chaos 21, 033120 (2011); http://dx.doi.org/10.1063/1.3629985 (12 pages)

Online Publication Date: 6 September 2011

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We analyze the response of rational and regular (hyperbolic-secant) soliton solutions of an extended nonlinear Schrödinger equation (NLSE) which includes an additional self-defocusing quadratic term, to periodic modulations of the coefficient in front of this term. Using the variational approximation (VA) with rational and hyperbolic trial functions, we transform this NLSE into Hamiltonian dynamical systems which give rise to chaotic solutions. The presence of chaos in the variational solutions is corroborated by calculating their power spectra and the correlation dimension of the Poincaré maps. This chaotic behavior (predicted by the VA) is not observed in the direct numerical solutions of the NLSE when rational initial conditions are used. The solitary-wave solutions generated by these initial conditions gradually decay under the action of the nonlinearity management. On the contrary, the solutions of the NLSE with exponentially localized initial conditions are robust solitary-waves with oscillations consistent with a chaotic or a complex quasiperiodic behavior.
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05.45.Yv Solitons
02.30.Hq Ordinary differential equations
02.30.Xx Calculus of variations

Robust outer synchronization between two complex networks with fractional order dynamics

Mohammad Mostafa Asheghan, Joaquín Míguez, Mohammad T. Hamidi-Beheshti, and Mohammad Saleh Tavazoei

Chaos 21, 033121 (2011); http://dx.doi.org/10.1063/1.3629986 (12 pages)

Online Publication Date: 7 September 2011

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Synchronization between two coupled complex networks with fractional-order dynamics, hereafter referred to as outer synchronization, is investigated in this work. In particular, we consider two systems consisting of interconnected nodes. The state variables of each node evolve with time according to a set of (possibly nonlinear and chaotic) fractional-order differential equations. One of the networks plays the role of a master system and drives the second network by way of an open-plus-closed-loop (OPCL) scheme. Starting from a simple analysis of the synchronization error and a basic lemma on the eigenvalues of matrices resulting from Kronecker products, we establish various sets of conditions for outer synchronization, i.e., for ensuring that the errors between the state variables of the master and response systems can asymptotically vanish with time. Then, we address the problem of robust outer synchronization, i.e., how to guarantee that the states of the nodes converge to common values when the parameters of the master and response networks are not identical, but present some perturbations. Assuming that these perturbations are bounded, we also find conditions for outer synchronization, this time given in terms of sets of linear matrix inequalities (LMIs). Most of the analytical results in this paper are valid both for fractional-order and integer-order dynamics. The assumptions on the inner (coupling) structure of the networks are mild, involving, at most, symmetry and diffusivity. The analytical results are complemented with numerical examples. In particular, we show examples of generalized and robust outer synchronization for networks whose nodes are governed by fractional-order Lorenz dynamics.
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05.45.Xt Synchronization; coupled oscillators
02.30.Hq Ordinary differential equations
05.45.-a Nonlinear dynamics and chaos

Lagrangian coherent structures are associated with fluctuations in airborne microbial populations

P. Tallapragada, S. D. Ross, and D. G. Schmale, III

Chaos 21, 033122 (2011); http://dx.doi.org/10.1063/1.3624930 (16 pages)

Online Publication Date: 9 September 2011

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Many microorganisms are advected in the lower atmosphere from one habitat to another with scales of motion being hundreds to thousands of kilometers. The concentration of these microbes in the lower atmosphere at a single geographic location can show rapid temporal changes. We used autonomous unmanned aerial vehicles equipped with microbe-sampling devices to collect fungi in the genus Fusarium 100 m above ground level at a single sampling location in Blacksburg, Virginia, USA. Some Fusarium species are important plant and animal pathogens, others saprophytes, and still others are producers of dangerous toxins. We correlated punctuated changes in the concentration of Fusarium to the movement of atmospheric transport barriers identified as finite-time Lyapunov exponent-based Lagrangian coherent structures (LCSs). An analysis of the finite-time Lyapunov exponent field for periods surrounding 73 individual flight collections of Fusarium showed a relationship between punctuated changes in concentrations of Fusarium and the passage times of LCSs, particularly repelling LCSs. This work has implications for understanding the atmospheric transport of invasive microbial species into previously unexposed regions and may contribute to information systems for pest management and disease control in the future.
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92.60.hg Constituent sources and sinks
93.30.Hf North America
92.60.Fm Boundary layer structure and processes

Synchronization of impulsively coupled complex systems with delay

Wen Sun, Francis Austin, Jinhu Lü, and Shihua Chen

Chaos 21, 033123 (2011); http://dx.doi.org/10.1063/1.3633081 (7 pages)

Online Publication Date: 14 September 2011

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This paper investigates the synchronization of complex systems with delay that are impulsively coupled at discrete instants only. Based on the comparison theorem of impulsive differential system, a distributed impulsive control scheme is proposed to achieve the synchronization for systems with delay. In the control strategy, the influence of all nodes to network synchronization relies on its weight. The proposed control scheme is applied to the chaotic delayed Hopfield neural networks and numerical simulations are presented to demonstrate the effectiveness of the proposed scheme.
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05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)
05.45.-a Nonlinear dynamics and chaos

Intrinsic noise induced resonance in presence of sub-threshold signal in Brusselator

Supravat Dey, Dibyendu Das, and P. Parmananda

Chaos 21, 033124 (2011); http://dx.doi.org/10.1063/1.3633477 (6 pages)

Online Publication Date: 14 September 2011

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In a system of non-linear chemical reactions called the Brusselator, we show that intrinsic noise can be regulated to drive it to exhibit resonance in the presence of a sub-threshold signal. The phenomena of periodic stochastic resonance and aperiodic stochastic resonance, hitherto studied mostly with extrinsic noise, is demonstrated here to occur with inherent systemic noise using exact stochastic simulation algorithm due to Gillespie. The role of intrinsic noise in a couple of other phenomena is also discussed.
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05.40.Ca Noise
05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)

Intermittent synchronization in a network of bursting neurons

Choongseok Park (박중석) and Leonid L. Rubchinsky

Chaos 21, 033125 (2011); http://dx.doi.org/10.1063/1.3633078 (14 pages)

Online Publication Date: 20 September 2011

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Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical network of the basal ganglia, formed by excitatory and inhibitory bursters of the subthalamic nucleus and globus pallidus, involved in motor control and affected in Parkinson’s disease. Recent experiments have demonstrated the intermittent nature of the phase-locking of neural activity in this network. Here, we explore one potential mechanism to explain the intermittent phase-locking in a network. We simplify the network to obtain a model of two inhibitory coupled elements and explore its dynamics. We used geometric analysis and singular perturbation methods for dynamical systems to reduce the full model to a simpler set of equations. Mathematical analysis was completed using three slow variables with two different time scales. Intermittently, synchronous oscillations are generated by overlapped spiking which crucially depends on the geometry of the slow phase plane and the interplay between slow variables as well as the strength of synapses. Two slow variables are responsible for the generation of activity patterns with overlapped spiking, and the other slower variable enhances the robustness of an irregular and intermittent activity pattern. While the analyzed network and the explored mechanism of intermittent synchrony appear to be quite generic, the results of this analysis can be used to trace particular values of biophysical parameters (synaptic strength and parameters of calcium dynamics), which are known to be impacted in Parkinson’s disease.
Show PACS
87.85.dq Neural networks
87.85.Wc Neural engineering
02.40.-k Geometry, differential geometry, and topology
87.19.X- Diseases
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