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Dec 2007

Volume 17, Issue 4, Articles (04xxxx)

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Chaos 17, 041104 (2007); http://dx.doi.org/10.1063/1.2776670 (1 page)

Luca Giomi and Mark Bowick
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Announcement: Focus issue on “Synchronization in complex networks”

Johan Suykens and Grigory Osipov

Chaos 17, 040201 (2007); http://dx.doi.org/10.1063/1.2811702 (1 page)

Online Publication Date: 15 November 2007

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01.10.Cr Announcements, news, and awards
05.45.Xt Synchronization; coupled oscillators
07.05.Mh Neural networks, fuzzy logic, artificial intelligence
01.75.+m Science and society
02.30.Oz Bifurcation theory
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Introduction: Fourth Annual Gallery of Nonlinear Images (Denver, Colorado, 2007)

Beate Schmittmann, M. Cristina Marchetti, Sidney Redner, and Arshad Kudrolli

Chaos 17, 041101 (2007); http://dx.doi.org/10.1063/1.2821617 (1 page)

Online Publication Date: 27 December 2007

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05.45.-a Nonlinear dynamics and chaos
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Polymer drop breakup in microchannels

P. E. Arratia, J. P. Gollub, and D. J. Durian

Chaos 17, 041102 (2007); http://dx.doi.org/10.1063/1.2786006 (1 page)

Online Publication Date: 27 December 2007

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47.57.Ng Polymers and polymer solutions
47.50.Ef Measurements
47.55.df Breakup and coalescence
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.80.Jk Flow visualization and imaging
47.85.Np Fluidics
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Rayleigh-Bénard convection with imposed heat flux

Hans Johnston and Charles R. Doering

Chaos 17, 041103 (2007); http://dx.doi.org/10.1063/1.2786003 (1 page) | Cited 2 times

Online Publication Date: 27 December 2007

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47.27.te Turbulent convective heat transfer
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Paraboloidal crystals

Luca Giomi and Mark Bowick

Chaos 17, 041104 (2007); http://dx.doi.org/10.1063/1.2776670 (1 page) | Cited 1 time

Online Publication Date: 27 December 2007

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61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling
82.70.Dd Colloids
87.15.A- Theory, modeling, and computer simulation
61.72.Bb Theories and models of crystal defects
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Shear faults in a model brittle solid

Craig E. Maloney and Mark O. Robbins

Chaos 17, 041105 (2007); http://dx.doi.org/10.1063/1.2786010 (1 page)

Online Publication Date: 27 December 2007

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46.50.+a Fracture mechanics, fatigue and cracks
61.43.-j Disordered solids
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Avoided level crossings in the quantization of a mixed regular-chaotic system

Thomas Mainiero and Mason A. Porter

Chaos 17, 041106 (2007); http://dx.doi.org/10.1063/1.2786009 (1 page)

Online Publication Date: 27 December 2007

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05.45.-a Nonlinear dynamics and chaos
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Spatially heterogeneous dynamics in a granular system near jamming

A. R. Abate and D. J. Durian

Chaos 17, 041107 (2007); http://dx.doi.org/10.1063/1.2786011 (1 page)

Online Publication Date: 27 December 2007

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81.90.+c Other topics in materials science (restricted to new topics in section 81)
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Complex pore spaces create record-breaking methane storage system for natural-gas vehicles

P. Pfeifer, L. Aston, M. Banks, S. Barker, J. Burress, S. Carter, J. Coleman, S. Crockett, C. Faulhaber, J. Flavin, M. Gordon, L. Hardcastle, Z. Kallenborn, M. Kemiki, C. Lapilli, et al.

Chaos 17, 041108 (2007); http://dx.doi.org/10.1063/1.2786007 (1 page) | Cited 1 time

Online Publication Date: 27 December 2007

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89.30.A- Fossil fuels
61.43.Gt Powders, porous materials
61.46.Df Structure of nanocrystals and nanoparticles ("colloidal" quantum dots but not gate-isolated embedded quantum dots)
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Numerical study of the phase space of modulated exponentially coupled harmonic oscillators

A. F. Isakovic

Chaos 17, 041109 (2007); http://dx.doi.org/10.1063/1.2779131 (1 page)

Online Publication Date: 27 December 2007

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05.45.-a Nonlinear dynamics and chaos
03.65.Ge Solutions of wave equations: bound states
02.30.Uu Integral transforms
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Characterization of stickiness by means of recurrence

Yong Zou, Marco Thiel, M. Carmen Romano, and Jürgen Kurths

Chaos 17, 043101 (2007); http://dx.doi.org/10.1063/1.2785159 (8 pages) | Cited 4 times

Online Publication Date: 12 October 2007

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We propose recurrence plots (RPs) to characterize the stickiness of a typical area-preserving map with coexisting chaotic and regular orbits. The difference of the recurrence properties between quasiperiodic and chaotic orbits is revisited, which helps to understand the complex patterns of the corresponding RPs. Moreover, several measures from the recurrence quantification analysis are used to quantify these patterns. Among these measures, the recurrence rate, quantifying the percentage of black points in the plot, is applied to characterize the stickiness of a typical chaotic orbit. The advantage of the recurrence based method in comparison to other standard techniques is that it is possible to distinguish between quasiperiodic and chaotic orbits that are temporarily trapped in a sticky domain, from very short trajectories.
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05.45.-a Nonlinear dynamics and chaos

Random walks on the Comb model and its generalizations

V. E. Arkhincheev

Chaos 17, 043102 (2007); http://dx.doi.org/10.1063/1.2772179 (7 pages) | Cited 2 times

Online Publication Date: 17 October 2007

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Microscopic models with anomalous diffusion, which include the Comb model and its generalization for the finite width of the backbone, have been considered in this paper. The physical mechanisms of the subdiffusion random walks have been established. The first comes from the permanent return of the diffusing particle to the initial point of the diffusion due to “effective reducing” of the dimensionality of the considered system to the quasi-one-dimensional system. This physical mechanism has been obtained in the Comb model and in the model with a strip. The second mechanism of the subdiffusion is connected with random capture on the traps of diffusing particles and their ensuing random release from the traps. It has been shown that these different mechanisms of subdiffusion have been described by the different generalized diffusion equations of fractional order. The solutions of these different equations have been obtained, and the physical sense of the fractional order generalized equations has been discussed.
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05.40.Fb Random walks and Levy flights
05.45.Df Fractals

Optimal structure of complex networks for minimizing traffic congestion

Liang Zhao, Thiago Henrique Cupertino, Kwangho Park, Ying-Cheng Lai, and Xiaogang Jin

Chaos 17, 043103 (2007); http://dx.doi.org/10.1063/1.2790367 (5 pages) | Cited 7 times

Online Publication Date: 17 October 2007

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To design complex networks to minimize traffic congestion, it is necessary to understand how traffic flow depends on network structure. We study data packet flow on complex networks, where the packet delivery capacity of each node is not fixed. The optimal configuration of capacities to minimize traffic congestion is derived and the critical packet generating rate is determined, below which the network is at a free flow state but above which congestion occurs. Our analysis reveals a direct relation between network topology and traffic flow. Optimal network structure, free of traffic congestion, should have two features: uniform distribution of load over all nodes and small network diameter. This finding is confirmed by numerical simulations. Our analysis also makes it possible to theoretically compare the congestion conditions for different types of complex networks. In particular, we find that network with low critical generating rate is more susceptible to congestion. The comparison has been made on the following complex-network topologies: random, scale-free, and regular.
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89.40.-a Transportation
84.30.Bv Circuit theory

On the absence of stable periodic orbits in domains of separatrix crossings in nonsymmetric slow-fast Hamiltonian systems

Anatoly Neishtadt and Alexei Vasiliev

Chaos 17, 043104 (2007); http://dx.doi.org/10.1063/1.2790368 (7 pages) | Cited 8 times

Online Publication Date: 17 October 2007

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We consider a two degree of freedom Hamiltonian system with one degree of freedom corresponding to fast motion and the other corresponding to slow motion. We assume that at frozen values of the slow variables there is a separatrix on the phase plane of the fast variables and there is a region in the phase space (the domain of separatrix crossings) where projections of phase points onto the plane of the fast variables repeatedly cross the separatrix in the process of evolution of the slow variables. Under rather general conditions, we prove that there are no stable periodic trajectories of any prescribed period inside the domain of separatrix crossings, except maybe for periodic trajectories passing anomalously close to the saddle point.
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45.05.+x General theory of classical mechanics of discrete systems
05.45.-a Nonlinear dynamics and chaos

Effect of dynamical traps on chaotic transport in a meandering jet flow

M. Yu. Uleysky, M. V. Budyansky, and S. V. Prants

Chaos 17, 043105 (2007); http://dx.doi.org/10.1063/1.2783258 (10 pages) | Cited 6 times

Online Publication Date: 18 October 2007

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We continue our study of chaotic mixing and transport of passive particles in a simple model of a meandering jet flow [ Prants et al., Chaos 16, 033117 (2006) ]. In the present paper we study and phenomenologically explain a connection between dynamical, topological, and statistical properties of chaotic mixing and transport in the model flow in terms of dynamical traps, singular zones in the phase space where particles may spend an arbitrarily long but finite time [ Zaslavsky, Phys. D 168–169, 292 (2002) ]. The transport of passive particles is described in terms of lengths and durations of zonal flights which are events between two successive changes of sign of zonal velocity. Some peculiarities of the respective probability density functions for short flights are proven to be caused by the so-called rotational-island traps connected with the boundaries of resonant islands (including the vortex cores) filled with the particles moving in the same frame and the saddle traps connected with periodic saddle trajectories. Whereas, the statistics of long flights can be explained by the influence of the so-called ballistic-islands traps filled with the particles moving from a frame to frame.
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47.52.+j Chaos in fluid dynamics
47.27.wg Turbulent jets
47.32.Ef Rotating and swirling flows
02.70.Rr General statistical methods

Enhancing dominant modes in nonstationary time series by means of the symbolic resonance analysis

Peter beim Graben, Heiner Drenhaus, Eva Brehm, Bela Rhode, Douglas Saddy, and Stefan Frisch

Chaos 17, 043106 (2007); http://dx.doi.org/10.1063/1.2795434 (13 pages) | Cited 2 times

Online Publication Date: 19 October 2007

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We present the symbolic resonance analysis (SRA) as a viable method for addressing the problem of enhancing a weakly dominant mode in a mixture of impulse responses obtained from a nonlinear dynamical system. We demonstrate this using results from a numerical simulation with Duffing oscillators in different domains of their parameter space, and by analyzing event-related brain potentials (ERPs) from a language processing experiment in German as a representative application. In this paradigm, the averaged ERPs exhibit an N400 followed by a sentence final negativity. Contemporary sentence processing models predict a late positivity (P600) as well. We show that the SRA is able to unveil the P600 evoked by the critical stimuli as a weakly dominant mode from the covering sentence final negativity.
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87.10.-e General theory and mathematical aspects
05.45.Tp Time series analysis
87.19.R- Mechanical and electrical properties of tissues and organs

Chaos suppression through asymmetric coupling

J. Bragard, G. Vidal, H. Mancini, C. Mendoza, and S. Boccaletti

Chaos 17, 043107 (2007); http://dx.doi.org/10.1063/1.2797378 (8 pages) | Cited 3 times

Online Publication Date: 22 October 2007

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We study pairs of identical coupled chaotic oscillators. In particular, we have used Roessler (in the funnel and no funnel regimes), Lorenz, and four-dimensional chaotic Lotka-Volterra models. In all four of these cases, a pair of identical oscillators is asymmetrically coupled. The main result of the numerical simulations is that in all cases, specific values of coupling strength and asymmetry exist that render the two oscillators periodic and synchronized. The values of the coupling strength for which this phenomenon occurs is well below the previously known value for complete synchronization. We have found that this behavior exists for all the chaotic oscillators that we have used in the analysis. We postulate that this behavior is presumably generic to all chaotic oscillators. In order to complete the study, we have tested the robustness of this phenomenon of chaos suppression versus the addition of some Gaussian noise. We found that chaos suppression is robust for the addition of finite noise level. Finally, we propose some extension to this research.
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05.45.Pq Numerical simulations of chaotic systems
05.45.Xt Synchronization; coupled oscillators
05.40.Ca Noise

On the complexity of periodic and nonperiodic behaviors of a hysteresis-based electronic oscillator

Daniele Stellardo, Federico Bizzarri, Marco Storace, and Oscar De Feo

Chaos 17, 043108 (2007); http://dx.doi.org/10.1063/1.2778552 (13 pages) | Cited 2 times

Online Publication Date: 24 October 2007

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We investigate the families of periodic and nonperiodic behaviors admitted by a hysteresis-based circuit oscillator. The analysis is carried out by combining brute-force simulations with continuation methods. As a result of the analysis, it is shown that the existence of many different periodic solutions and of the chaotic behaviors associated with them is organized by few codimension-2 bifurcation points. This implies the possibility of switching between different periodic solutions by controlling only two bifurcation parameters, which makes the oscillator a possible generator of nontrivial periodic solutions suitable, for instance for actual radiofrequency identification systems applications.
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05.45.-a Nonlinear dynamics and chaos
84.30.Ng Oscillators, pulse generators, and function generators

Chaotic oscillations in a map-based model of neural activity

M. Courbage, V. I. Nekorkin, and L. V. Vdovin

Chaos 17, 043109 (2007); http://dx.doi.org/10.1063/1.2795435 (13 pages) | Cited 7 times

Online Publication Date: 26 October 2007

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We propose a discrete time dynamical system (a map) as a phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find conditions under which this map has an invariant region on the phase plane, containing a chaotic attractor. This attractor creates chaotic spiking-bursting oscillations of the model. We also show various regimes of other neural activities (subthreshold oscillations, phasic spiking, etc.) derived from the proposed model.
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87.10.-e General theory and mathematical aspects
05.45.-a Nonlinear dynamics and chaos
87.18.Sn Neural networks and synaptic communication

Multiscale vulnerability of complex networks

Stefano Boccaletti, Javier Buldú, Regino Criado, Julio Flores, Vito Latora, Javier Pello, and Miguel Romance

Chaos 17, 043110 (2007); http://dx.doi.org/10.1063/1.2801687 (4 pages) | Cited 4 times

Online Publication Date: 26 October 2007

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We present a novel approach to quantify the vulnerability of a complex network, i.e., the capacity of a graph to maintain its functional performance under random damages or malicious attacks. The proposed measure represents a multiscale evaluation of vulnerability, and makes use of combined powers of the links’ betweenness. We show that the proposed approach is able to properly describe some cases for which earlier measures of vulnerability fail. The relevant applications of our method for technological network design are outlined.
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05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.10.Ox Combinatorics; graph theory

Frequency dependence of phase-synchronization time in nonlinear dynamical systems

Kwangho Park, Ying-Cheng Lai, and Satish Krishnamoorthy

Chaos 17, 043111 (2007); http://dx.doi.org/10.1063/1.2802544 (5 pages) | Cited 3 times

Online Publication Date: 15 November 2007

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It has been found recently that the averaged phase-synchronization time between the input and the output signals of a nonlinear dynamical system can exhibit an extremely high sensitivity to variations in the noise level. In real-world signal-processing applications, sensitivity to frequency variations may be of considerable interest. Here we investigate the dependence of the averaged phase-synchronization time on frequency of the input signal. Our finding is that, for typical nonlinear oscillator systems, there can be a frequency regime where the time exhibits significant sensitivity to frequency variations. We obtain an analytic formula to quantify the frequency dependence, provide numerical support, and present experimental evidence from a simple nonlinear circuit system.
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05.45.Xt Synchronization; coupled oscillators

Deterministic single-file dynamics in collisional representation

F. Marchesoni and A. Taloni

Chaos 17, 043112 (2007); http://dx.doi.org/10.1063/1.2803718 (10 pages) | Cited 2 times

Online Publication Date: 15 November 2007

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We re-examine numerically the diffusion of a deterministic, or ballistic single file with preassigned velocity distribution (Jepsen’s gas) from a collisional viewpoint. For a two-modal velocity distribution, where half the particles have velocity ±c, the collisional statistics is analytically proven to reproduce the continuous time representation. For a three-modal velocity distribution with equal fractions, where less than 1/2 of the particles have velocity ±c, with the remaining particles at rest, the collisional process is shown to be inhomogeneous; its stationary properties are discussed here by combining exact and phenomenological arguments. Collisional memory effects are then related to the negative power-law tails in the velocity autocorrelation functions, predicted earlier in the continuous time formalism. Numerical and analytical results for Gaussian and four-modal Jepsen’s gases are also reported for the sake of a comparison.
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05.60.-k Transport processes
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.50.-r Probability theory, stochastic processes, and statistics
02.60.-x Numerical approximation and analysis

Detecting and localizing the foci in human epileptic seizures

Eshel Ben-Jacob, Stefano Boccaletti, Anna Pomyalov, Itamar Procaccia, and Vernon L. Towle

Chaos 17, 043113 (2007); http://dx.doi.org/10.1063/1.2805658 (8 pages) | Cited 7 times

Online Publication Date: 15 November 2007

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We consider the electrical signals recorded from a subdural array of electrodes placed on the pial surface of the brain for chronic evaluation of epileptic patients before surgical resection. A simple and computationally fast method to analyze the interictal phase synchrony between such electrodes is introduced and developed with the aim of detecting and localizing the foci of the epileptic seizures. We evaluate the method by comparing the results of surgery to the localization predicted here. We find an indication of good correspondence between the success or failure in the surgery and the agreement between our identification and the regions actually operated on.
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87.19.L- Neuroscience
87.19.X- Diseases

Quantifying the complexity of excised larynx vibrations from high-speed imaging using spatiotemporal and nonlinear dynamic analyses

Yu Zhang, Jack J. Jiang, Chao Tao, Erik Bieging, and Julia K. MacCallum

Chaos 17, 043114 (2007); http://dx.doi.org/10.1063/1.2784384 (10 pages) | Cited 7 times

Online Publication Date: 15 November 2007

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In this paper, we investigate the biomechanical applications of spatiotemporal analysis and nonlinear dynamic analysis to quantitatively describe regular and irregular vibrations of twelve excised larynges from high-speed image recordings. Regular vibrations show simple spatial symmetry, temporal periodicity, and discrete frequency spectra, while irregular vibrations show complex spatiotemporal plots, aperiodic time series, and broadband spectra. Furthermore, the global entropy and correlation length from spatiotemporal analysis and the correlation dimension from nonlinear dynamic analysis reveal a statistical difference between regular and irregular vibrations. In comparison with regular vibrations, the global entropy and correlation dimension of irregular vibrations are statistically higher, while the correlation length is significantly lower. These findings show that spatiotemporal analysis and nonlinear dynamic analysis are capable of describing the complex dynamics of vocal fold vibrations from high-speed imaging and may potentially be helpful for understanding disordered behaviors in biomedical laryngeal systems.
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87.19.rs Movement
87.19.ru Locomotion
87.63.L- Visual imaging
05.45.Tp Time series analysis

Vulnerability to re-entry in simulated two-dimensional cardiac tissue: Effects of electrical restitution and stimulation sequence

Diana X. Tran, Ming-Jim Yang, James N. Weiss, Alan Garfinkel, and Zhilin Qu

Chaos 17, 043115 (2007); http://dx.doi.org/10.1063/1.2784387 (11 pages) | Cited 4 times

Online Publication Date: 15 November 2007

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Ventricular fibrillation is a lethal arrhythmia characterized by multiple wavelets usually starting from a single or figure-of-eight re-entrant circuit. Understanding the factors regulating vulnerability to the re-entry is essential for developing effective therapeutic strategies to prevent ventricular fibrillation. In this study, we investigated how pre-existing tissue heterogeneities and electrical restitution properties affect the initiation of re-entry by premature extrastimuli in two-dimensional cardiac tissue models. We studied two pacing protocols for inducing re-entry following the “sinus” rhythm (S1) beat: (1) a single premature (S2) extrastimulus in heterogeneous tissue; (2) two premature extrastimuli (S2 and S3) in homogeneous tissue. In the first case, the vulnerable window of re-entry is determined by the spatial dimension and extent of the heterogeneity, and is also affected by electrical restitution properties and the location of the premature stimulus. The vulnerable window first increases as the action potential duration (APD) difference between the inside and outside of the heterogeneous region increases, but then decreases as this difference increases further. Steeper APD restitution reduces the vulnerable window of re-entry. In the second case, electrical restitution plays an essential role. When APD restitution is flat, no re-entry can be induced. When APD restitution is steep, re-entry can be induced by an S3 over a range of S1S2 intervals, which is also affected by conduction velocity restitution. When APD restitution is even steeper, the vulnerable window is reduced due to collision of the spiral tips.
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87.19.R- Mechanical and electrical properties of tissues and organs
87.10.-e General theory and mathematical aspects
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