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Dec 2009

Volume 19, Issue 4, Articles (04xxxx)

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Chaos 19, 041102 (2009); http://dx.doi.org/10.1063/1.3176902 (1 page)

G. Seiden, S. Weiss, and E. Bodenschatz
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Introduction: Sixth Annual Gallery of Nonlinear Images (Pittsburgh, Pennsylvania, 2009)

Predrag Cvitanović, Karen E. Daniels, Arshad Kudrolli, Wolfgang Losert, and Sidney Redner

Chaos 19, 041101 (2009); http://dx.doi.org/10.1063/1.3257679 (1 page)

Online Publication Date: 27 October 2009

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01.10.Cr Announcements, news, and awards
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Superlattice patterns in forced thermal convection

G. Seiden, S. Weiss, and E. Bodenschatz

Chaos 19, 041102 (2009); http://dx.doi.org/10.1063/1.3176902 (1 page) | Cited 1 time

Online Publication Date: 27 October 2009

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47.27.te Turbulent convective heat transfer
47.54.-r Pattern selection; pattern formation
05.45.-a Nonlinear dynamics and chaos
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Rupture and clustering in granular streams

John R. Royer, Loreto Oyarte, Matthias E. Möbius, and Heinrich M. Jaeger

Chaos 19, 041103 (2009); http://dx.doi.org/10.1063/1.3211191 (1 page)

Online Publication Date: 27 October 2009

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68.03.Cd Surface tension and related phenomena
62.10.+s Mechanical properties of liquids
47.55.D- Drops and bubbles
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Visualization of communities in networks

Amanda L. Traud, Christina Frost, Peter J. Mucha, and Mason A. Porter

Chaos 19, 041104 (2009); http://dx.doi.org/10.1063/1.3194108 (1 page) | Cited 3 times

Online Publication Date: 27 October 2009

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01.75.+m Science and society
89.20.-a Interdisciplinary applications of physics
89.65.Ef Social organizations; anthropology
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The mayonnaise droplet

D. Terwagne, N. Mack, S. Dorbolo, T. Gilet, J.-Y. Raty, and N. Vandewalle

Chaos 19, 041105 (2009); http://dx.doi.org/10.1063/1.3202626 (1 page) | Cited 1 time

Online Publication Date: 27 October 2009

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82.70.Kj Emulsions and suspensions
47.55.D- Drops and bubbles
66.20.Ej Studies of viscosity and rheological properties of specific liquids
85.85.+j Micro- and nano-electromechanical systems (MEMS/NEMS) and devices
63.50.-x Vibrational states in disordered systems
47.52.+j Chaos in fluid dynamics
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Unstable Kolmogorov flow in granular matter

Klaus Roeller, Jürgen Vollmer, and Stephan Herminghaus

Chaos 19, 041106 (2009); http://dx.doi.org/10.1063/1.3202616 (1 page) | Cited 1 time

Online Publication Date: 27 October 2009

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47.57.Gc Granular flow
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.11.Mn Molecular dynamics methods
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Force network ensemble for the triangular lattice: A tale of tiles

Brian P. Tighe, Adrianne R. T. van Eerd, and Thijs J. H. Vlugt

Chaos 19, 041107 (2009); http://dx.doi.org/10.1063/1.3207833 (1 page)

Online Publication Date: 27 October 2009

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45.70.-n Granular systems
46.55.+d Tribology and mechanical contacts
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
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Generating ensembles of two-dimensional granular configurations

James G. Puckett, Frédéric Lechenault, and Karen E. Daniels

Chaos 19, 041108 (2009); http://dx.doi.org/10.1063/1.3207830 (1 page)

Online Publication Date: 27 October 2009

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81.05.Rm Porous materials; granular materials
64.70.ps Granules
66.30.-h Diffusion in solids
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X-ray computerized tomography scan of crumpled aluminum sheet

Anne Dominique Cambou and Narayanan Menon

Chaos 19, 041109 (2009); http://dx.doi.org/10.1063/1.3212924 (1 page)

Online Publication Date: 27 October 2009

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81.70.Tx Computed tomography
07.85.Tt X-ray microscopes
42.30.Wb Image reconstruction; tomography
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The adventures of Dicty, the Dictyostelium cell

Meghan Driscoll, Rael Kopace, Linjie Li, Colin McCann, John Watts, John T. Fourkas, and Wolfgang Losert

Chaos 19, 041110 (2009); http://dx.doi.org/10.1063/1.3212926 (1 page)

Online Publication Date: 27 October 2009

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87.17.Jj Cell locomotion, chemotaxis
87.15.rp Polymerization
87.15.M- Spectra of biomolecules
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VORO++: A three-dimensional Voronoi cell library in C++

Chris H. Rycroft

Chaos 19, 041111 (2009); http://dx.doi.org/10.1063/1.3215722 (1 page)

Online Publication Date: 27 October 2009

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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
07.05.Rm Data presentation and visualization: algorithms and implementation
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Homogenous dislocation nucleation

Asad Hasan and Craig E. Maloney

Chaos 19, 041112 (2009); http://dx.doi.org/10.1063/1.3216852 (1 page)

Online Publication Date: 27 October 2009

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61.72.Lk Linear defects: dislocations, disclinations
62.25.-g Mechanical properties of nanoscale systems
61.72.Bb Theories and models of crystal defects
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Discrete instability in the DNA double helix

Conrad Bertrand Tabi, Alidou Mohamadou, and Timoléon Crépin Kofané

Chaos 19, 043101 (2009); http://dx.doi.org/10.1063/1.3234244 (13 pages) | Cited 3 times

Online Publication Date: 5 October 2009

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Modulational instability (MI) is explored in the framework of the base-rotor model of DNA dynamics. We show, in fact, that the helicoidal coupling introduced in the spin model of DNA reduces the system to a modified discrete sine-Gordon (sG) equation. The MI criterion is thus modified and displays interesting features because of the helicoidal coupling. In the simulations, we have found that a train of pulses is generated when the lattice is subjected to MI, in agreement with analytical results obtained in a modified discrete sG equation. Also, the competitive effects of the harmonic longitudinal and helicoidal constants on the dynamics of the system are notably pointed out. In the same way, it is shown that MI can lead to energy localization which becomes high for some values of the helicoidal coupling constant.
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87.14.gk DNA
36.20.Hb Configuration (bonds, dimensions)
87.15.B- Structure of biomolecules
87.15.H- Dynamics of biomolecules

Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach

Jorge Duarte, Cristina Januário, Nuno Martins, and Josep Sardanyés

Chaos 19, 043102 (2009); http://dx.doi.org/10.1063/1.3243924 (12 pages) | Cited 2 times

Online Publication Date: 12 October 2009

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In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction σ of predators cooperates in prey’s hunting, while the rest of the population 1−σ hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K,C0) and (K,σ) which separates two scenarios: (i) all-species coexistence and (ii) predator’s extinction via chaotic crisis. We show that the crisis value of the carrying capacity Kc decreases at increasing σ, indicating that predator’s populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.
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05.45.-a Nonlinear dynamics and chaos
89.75.-k Complex systems
02.40.Re Algebraic topology
05.70.Ce Thermodynamic functions and equations of state

Permutations and time series analysis

Jose S. Cánovas and Antonio Guillamón

Chaos 19, 043103 (2009); http://dx.doi.org/10.1063/1.3238256 (12 pages)

Online Publication Date: 13 October 2009

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The main aim of this paper is to show how the use of permutations can be useful in the study of time series analysis. In particular, we introduce a test for checking the independence of a time series which is based on the number of admissible permutations on it. The main improvement in our tests is that we are able to give a theoretical distribution for independent time series.
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05.45.Tp Time series analysis
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.50.-r Probability theory, stochastic processes, and statistics

Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action

Seth A. Marvel, Renato E. Mirollo, and Steven H. Strogatz

Chaos 19, 043104 (2009); http://dx.doi.org/10.1063/1.3247089 (11 pages) | Cited 13 times

Online Publication Date: 15 October 2009

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Systems of N identical phase oscillators with global sinusoidal coupling are known to display low-dimensional dynamics. Although this phenomenon was first observed about 20 years ago, its underlying cause has remained a puzzle. Here we expose the structure working behind the scenes of these systems by proving that the governing equations are generated by the action of the Möbius group, a three-parameter subgroup of fractional linear transformations that map the unit disk to itself. When there are no auxiliary state variables, the group action partitions the N-dimensional state space into three-dimensional invariant manifolds (the group orbits). The N−3 constants of motion associated with this foliation are the N−3 functionally independent cross ratios of the oscillator phases. No further reduction is possible, in general; numerical experiments on models of Josephson junction arrays suggest that the invariant manifolds often contain three-dimensional regions of neutrally stable chaos.
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05.45.Xt Synchronization; coupled oscillators
02.20.-a Group theory

Two routes to the one-dimensional discrete nonpolynomial Schrödinger equation

G. Gligorić, A. Maluckov, L. Salasnich, B. A. Malomed, and Lj. Hadžievski

Chaos 19, 043105 (2009); http://dx.doi.org/10.1063/1.3248269 (7 pages)

Online Publication Date: 15 October 2009

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The Bose–Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schrödinger equation (NPSE). Both models are derived from the three-dimensional Gross–Pitaevskii equation (3D GPE). To produce “model 1” (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. “Model 2,” which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2—in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.
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03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations
05.45.Yv Solitons
42.50.Wk Mechanical effects of light on material media, microstructures and particles
37.10.Jk Atoms in optical lattices

The compass rose pattern in electricity prices

Jonathan A. Batten and Mahmoud Hamada

Chaos 19, 043106 (2009); http://dx.doi.org/10.1063/1.3243920 (15 pages) | Cited 1 time

Online Publication Date: 16 October 2009

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The “compass rose pattern” is known to appear in the phase portraits, or scatter diagrams, of the high-frequency returns of financial series. We first show that this pattern is also present in the returns of spot electricity prices. Early researchers investigating these phenomena hoped that these patterns signaled the presence of rich dynamics, possibly chaotic or fractal in nature. Although there is a definite autoregressive and conditional heteroscedasticity structure in electricity returns, we find that after simple filtering no pattern remains. While the series is non-normal in terms of their distribution and statistical tests fail to identify significant chaos, there is evidence of fractal structures in periodic price returns when measured over the trading day. The phase diagram of the filtered returns provides a useful visual check on independence, a property necessary for pricing and trading derivatives and portfolio construction, as well as providing useful insights into the market dynamics.
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84.70.+p High-current and high-voltage technology: power systems; power transmission lines and cables
02.50.-r Probability theory, stochastic processes, and statistics

The impact of risk-averse operation on the likelihood of extreme events in a simple model of infrastructure

B. A. Carreras, D. E. Newman, Ian Dobson, and Matthew Zeidenberg

Chaos 19, 043107 (2009); http://dx.doi.org/10.1063/1.3234238 (8 pages)

Online Publication Date: 20 October 2009

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A simple dynamic model of agent operation of an infrastructure system is presented. This system evolves over a long time scale by a daily increase in consumer demand that raises the overall load on the system and an engineering response to failures that involves upgrading of the components. The system is controlled by adjusting the upgrading rate of the components and the replacement time of the components. Two agents operate the system. Their behavior is characterized by their risk-averse and risk-taking attitudes while operating the system, their response to large events, and the effect of learning time on adapting to new conditions. A risk-averse operation causes a reduction in the frequency of failures and in the number of failures per unit time. However, risk aversion brings an increase in the probability of extreme events.
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89.75.Hc Networks and genealogical trees
89.20.Ff Computer science and technology

Transport properties in nontwist area-preserving maps

J. D. Szezech, I. L. Caldas, S. R. Lopes, R. L. Viana, and P. J. Morrison

Chaos 19, 043108 (2009); http://dx.doi.org/10.1063/1.3247349 (9 pages) | Cited 12 times

Online Publication Date: 23 October 2009

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Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds.
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47.52.+j Chaos in fluid dynamics
47.27.N- Wall-bounded shear flow turbulence
52.25.Gj Fluctuation and chaos phenomena
52.25.Fi Transport properties

Fixed points, stable manifolds, weather regimes, and their predictability

Bruno Deremble, Fabio D’Andrea, and Michael Ghil

Chaos 19, 043109 (2009); http://dx.doi.org/10.1063/1.3230497 (20 pages) | Cited 1 time

Online Publication Date: 27 October 2009

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In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model’s fixed points in phase space. The model dynamics is characterized by the coexistence of multiple “weather regimes.” To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, “bred vectors” and singular vectors. These results are then verified in the framework of ensemble forecasts issued from “clouds” (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.
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92.60.Wc Weather analysis and prediction
05.45.-a Nonlinear dynamics and chaos
92.60.Aa Modeling and model calibration

Accurate noise projection for reduced stochastic epidemic models

Eric Forgoston, Lora Billings, and Ira B. Schwartz

Chaos 19, 043110 (2009); http://dx.doi.org/10.1063/1.3247350 (15 pages) | Cited 4 times

Online Publication Date: 29 October 2009

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We consider a stochastic susceptible-exposed-infected-recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the associated, reduced set of stochastic evolution equations. The transformation correctly projects both the dynamics and the noise onto the center manifold. Therefore, the solution of this reduced stochastic dynamical system yields excellent agreement, both in amplitude and phase, with the solution of the original stochastic system for a temporal scale that is orders of magnitude longer than the typical relaxation time. This new method allows for improved time series prediction of the number of infectious cases when modeling the spread of disease in a population. Numerical solutions of the fluctuations of the SEIR model are considered in the infinite population limit using a Langevin equation approach, as well as in a finite population simulated as a Markov process.
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87.10.Mn Stochastic modeling
02.50.Ga Markov processes
87.23.Cc Population dynamics and ecological pattern formation
87.19.X- Diseases
02.50.Ey Stochastic processes

Bifurcation and chaos in spin-valve pillars in a periodic applied magnetic field

S. Murugesh and M. Lakshmanan

Chaos 19, 043111 (2009); http://dx.doi.org/10.1063/1.3258365 (7 pages) | Cited 4 times

Online Publication Date: 3 November 2009

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We study the bifurcation and chaos scenario of the macromagnetization vector in a homogeneous nanoscale-ferromagnetic thin film of the type used in spin-valve pillars. The underlying dynamics is described by a generalized Landau–Lifshitz–Gilbert (LLG) equation. The LLG equation has an especially appealing form under a complex stereographic projection, wherein the qualitative equivalence of an applied field and a spin-current induced torque is transparent. Recently, chaotic behavior of such a spin vector has been identified by Li et al. [ Li et al.Phys. Rev. B 74, 054417 (2006) ] using a spin-polarized current passing through the pillar of constant polarization direction and periodically varying magnitude, owing to the spin-transfer torque effect. In this paper, we show that the same dynamical behavior can be achieved using a periodically varying applied magnetic field in the presence of a constant dc magnetic field and constant spin current, which is technically much more feasible, and demonstrate numerically the chaotic dynamics in the system for an infinitely thin film. Further, it is noted that in the presence of a nonzero crystal anisotropy field, chaotic dynamics occurs at much lower magnitudes of the spin current and dc applied field.
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75.70.Ak Magnetic properties of monolayers and thin films
75.47.De Giant magnetoresistance
85.75.-d Magnetoelectronics; spintronics: devices exploiting spin polarized transport or integrated magnetic fields
75.30.Gw Magnetic anisotropy
75.50.Tt Fine-particle systems; nanocrystalline materials
72.25.-b Spin polarized transport

Chaoticity of the blood cell production system

Ryszard Rudnicki

Chaos 19, 043112 (2009); http://dx.doi.org/10.1063/1.3258364 (6 pages)

Online Publication Date: 6 November 2009

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We present a structured model of stem cells given by a partial differential equation. This equation generates a semiflow acting on the set of densities. We show that this semiflow possesses an invariant exact measure positive on open sets. From this it follows that the system is chaotic, i.e., it has dense trajectories and each trajectory is unstable.
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87.10.Ed Ordinary differential equations (ODE), partial differential equations (PDE), integrodifferential models
87.10.Mn Stochastic modeling
87.19.U- Hemodynamics
87.19.rh Fluid transport and rheology

Synchronization in coupled time-delayed systems with parameter mismatch and noise perturbation

Yongzheng Sun and Jiong Ruan

Chaos 19, 043113 (2009); http://dx.doi.org/10.1063/1.3262488 (10 pages) | Cited 8 times

Online Publication Date: 11 November 2009

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In this paper, a design of coupling and effective sufficient condition for stable complete synchronization and antisynchronization of a class of coupled time-delayed systems with parameter mismatch and noise perturbation are established. Based on the LaSalle-type invariance principle for stochastic differential equations, sufficient conditions guaranteeing complete synchronization and antisynchronization with constant time delay are developed. Also delay-dependent sufficient conditions for the case of time-varying delay are derived by using the Lyapunov approach for stochastic differential equations. Numerical examples fully support the analytical results.
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02.30.Yy Control theory
02.30.Jr Partial differential equations
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