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Announcement: Focus Issue on “Dynamics in Systems Biology”

C. A. Brackley, O. Ebenhöh, C. Grebogi, A. Moura, M. C. Romano, M. Thiel, and J. Kurths

Chaos 20, 010201 (2010); http://dx.doi.org/10.1063/1.3293069 (1 page)

Online Publication Date: 14 January 2010

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01.10.Cr

Announcements, news, and awards

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Announcement: Focus Issue on “Mesoscales in Complex Networks”

J. A. Almendral, R. Criado, I. Leyva, J. M. Buldú, and I. Sendiña Nadal

Chaos 20, 010202 (2010); http://dx.doi.org/10.1063/1.3298887 (1 page)

Online Publication Date: 19 January 2010

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01.10.Cr	Announcements, news, and awards
89.75.Fb	Structures and organization in complex systems
89.75.Da	Systems obeying scaling laws
89.75.Hc	Networks and genealogical trees

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Lobe transport analysis of the Kelvin–Stuart cat’s eyes driven flow

Stephen M. Rodrigue and Elia V. Eschenazi

Chaos 20, 013101 (2010); http://dx.doi.org/10.1063/1.3272714 (13 pages)

Online Publication Date: 5 January 2010

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Mixing and transport in the driven Kelvin–Stuart cat’s eyes dynamical system is studied using lobe transport theory and the topological approximation method (TAM). The application of the TAM also provides a global bifurcation analysis. Lobe areas are calculated using the Melnikov amplitude function, which has been derived for the Kelvin–Stuart system. Results indicate that regions, originally in the exterior above the vortex chain, can be transported to the exterior below the vortex chain (and vice versa) by passing through the interior, and that a region within the interior of a given vortex can be transported to the interior of a neighboring vortex, or the interior of a vortex several vortices distant from the given vortex. Cumulative transport is shown to decrease with increasing perturbation frequency for a fixed value of perturbation strength. Cumulative transport increases with increasing perturbation strength for a fixed value of the structure index L. Cumulative transport approaches a characteristic maximum value for each set of parameter values. Results demonstrate a linear dependence of the maximum cumulative transport upon a universal flux function of the form proposed by Rom-Kedar and Poje, suggesting a possible scaling in the transport dependent on the structure index L.

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47.32.-y	Vortex dynamics; rotating fluids
47.27.W-	Boundary-free shear flow turbulence

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Generation of solitons and breathers in the extended Korteweg–de Vries equation with positive cubic nonlinearity

R. Grimshaw, A. Slunyaev, and E. Pelinovsky

Chaos 20, 013102 (2010); http://dx.doi.org/10.1063/1.3279480 (11 pages) | Cited 6 times

Online Publication Date: 5 January 2010

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The initial-value problem for box-like initial disturbances is studied within the framework of an extended Korteweg–de Vries equation with both quadratic and cubic nonlinear terms, also known as the Gardner equation, for the case when the cubic nonlinear coefficient has the same sign as the linear dispersion coefficient. The discrete spectrum of the associated scattering problem is found, which is used to describe the asymptotic solution of the initial-value problem. It is found that while initial disturbances of the same sign as the quadratic nonlinear coefficient result in generation of only solitons, the case of the opposite polarity of the initial disturbance has a variety of possible outcomes. In this case solitons of different polarities as well as breathers may occur. The bifurcation point when two eigenvalues corresponding to solitons merge to the eigenvalues associated with breathers is considered in more detail. Direct numerical simulations show that breathers and soliton pairs of different polarities can appear from a simple box-like initial disturbance.

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05.45.Yv	Solitons
02.60.-x	Numerical approximation and analysis
02.30.Oz	Bifurcation theory
05.45.-a	Nonlinear dynamics and chaos
02.10.Ud	Linear algebra

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The stability of adaptive synchronization of chaotic systems

Francesco Sorrentino, Gilad Barlev, Adam B. Cohen, and Edward Ott

Chaos 20, 013103 (2010); http://dx.doi.org/10.1063/1.3279646 (10 pages) | Cited 8 times

Online Publication Date: 14 January 2010

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In past works, various schemes for adaptive synchronization of chaotic systems have been proposed. The stability of such schemes is central to their utilization. As an example addressing this issue, we consider a recently proposed adaptive scheme for maintaining the synchronized state of identical coupled chaotic systems in the presence of a priori unknown slow temporal drift in the couplings. For this illustrative example, we develop an extension of the master stability function technique to study synchronization stability with adaptive coupling. Using this formulation, we examine the local stability of synchronization for typical chaotic orbits and for unstable periodic orbits within the synchronized chaotic attractor (bubbling). Numerical experiments illustrating the results are presented. We observe that the stable range of synchronism can be sensitively dependent on the adaptation parameters, and we discuss the strong implication of bubbling for practically achievable adaptive synchronization. We also find that for our coupled systems with adaptation, bubbling can be caused by a slow temporal drift in the coupling strength.

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05.45.Xt

Synchronization; coupled oscillators

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Weak signal detection based on the information fusion and chaotic oscillator

Xiuqiao Xiang and Baochang Shi

Chaos 20, 013104 (2010); http://dx.doi.org/10.1063/1.3279568 (6 pages)

Online Publication Date: 19 January 2010

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Based on the chaotic oscillator, a method for weak signal detection using information fusion technology is proposed in this paper. On the one hand, various methods are employed to the amplitude detection of the same weak periodic signal, then the detection outcomes are fused by the adaptive weighted fusion method. On the other hand, during the detection course, information entropy, statistic distance, and Walsh transform are, respectively, used in the state recognition of chaotic oscillator from the viewpoint of time domain or frequency domain, then the recognition results are fused by the k/l fusion method. Numerical results show that the proposed approach detects signal more precisely, identifies state more accurately, and represents information more completely compared with traditional methods.

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84.40.Ua	Telecommunications: signal transmission and processing; communication satellites
05.45.Xt	Synchronization; coupled oscillators
02.30.Uu	Integral transforms

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Chaotic operation by a single transistor circuit in the reverse active region

M. P. Hanias, I. L. Giannis, and G. S. Tombras

Chaos 20, 013105 (2010); http://dx.doi.org/10.1063/1.3293133 (7 pages)

Online Publication Date: 20 January 2010

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In this paper, we present an externally triggered experimental chaotic circuit with a bipolar junction transistor operating in its reverse active region in order to investigate for possible control features in its output phase portraits. Nonlinear time series modeling techniques are applied to analyze the circuit’s output voltage oscillations and reveal the presence of chaos, while the chaos itself is achieved by controlling the amplitude of the applied input signal. The phase space, which describes the behavior evolution of a nonlinear system, is reconstructed using the delay embedding theorem suggested by Takens. The time delay used for this reconstruction is chosen after examining the first minimum of the collected data average mutual information, while the sufficient embedding dimension is estimated using the false nearest-neighbor algorithm which has a value of 5. Also the largest Lyapunov exponent is estimated and found equal to 0.020 48. Finally, the phase space embedding based weight predictor algorithm is employed to make a short-term prediction of the chaotic time series for which the system’s governing equations may be unknown.

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85.30.Pq	Bipolar transistors
02.50.-r	Probability theory, stochastic processes, and statistics

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Geometry of repeated measurements in chaotic systems

P.-M. Binder and B. D. Wissman

Chaos 20, 013106 (2010); http://dx.doi.org/10.1063/1.3298244 (6 pages)

Online Publication Date: 26 January 2010

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We use joint probability matrices for measurements at different times to describe chaotic systems. By coarse graining the range of the measured variable into uniformly sized bins we can generate matrices that contain both topological and metric information about the systems being studied. Armed with this tool we examine two extreme families of chaotic systems. In the case of one-dimensional piecewise linear maps, we can construct transfer matrices that depend on the map and partition used, and which allow us to generate the respective joint probability matrices for all times as well as the exact time evolution of the mutual information function. We find that the mutual information decays linearly or exponentially depending on whether the second-largest eigenvalue of the transfer matrix is zero or not. In the case of three-dimensional, continuous-time chaotic systems we generate the joint probability matrices directly from numerical data. We show that these matrices directly provide attractor reconstructions with information about the attractor’s probability measure.

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05.45.-a	Nonlinear dynamics and chaos
02.10.Yn	Matrix theory
02.40.-k	Geometry, differential geometry, and topology
02.50.Cw	Probability theory

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An automated algorithm for the generation of dynamically reconstructed trajectories

C. Komalapriya, M. C. Romano, M. Thiel, N. Marwan, J. Kurths, I. Z. Kiss, and J. L. Hudson

Chaos 20, 013107 (2010); http://dx.doi.org/10.1063/1.3279680 (9 pages)

Online Publication Date: 3 February 2010

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The lack of long enough data sets is a major problem in the study of many real world systems. As it has been recently shown [ C. Komalapriya, M. Thiel, M. C. Romano, N. Marwan, U. Schwarz, and J. Kurths, Phys. Rev. E 78, 066217 (2008) ], this problem can be overcome in the case of ergodic systems if an ensemble of short trajectories is available, from which dynamically reconstructed trajectories can be generated. However, this method has some disadvantages which hinder its applicability, such as the need for estimation of optimal parameters. Here, we propose a substantially improved algorithm that overcomes the problems encountered by the former one, allowing its automatic application. Furthermore, we show that the new algorithm not only reproduces the short term but also the long term dynamics of the system under study, in contrast to the former algorithm. To exemplify the potential of the new algorithm, we apply it to experimental data from electrochemical oscillators and also to analyze the well-known problem of transient chaotic trajectories.

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82.40.Bj	Oscillations, chaos, and bifurcations
05.45.Tp	Time series analysis
82.45.-h	Electrochemistry and electrophoresis

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Metastable chimera states in community-structured oscillator networks

Murray Shanahan

Chaos 20, 013108 (2010); http://dx.doi.org/10.1063/1.3305451 (5 pages) | Cited 1 time

Online Publication Date: 22 February 2010

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A system of symmetrically coupled identical oscillators with phase lag is presented, which is capable of generating a large repertoire of transient (metastable) “chimera” states in which synchronization and desynchronization coexist. The oscillators are organized into communities, such that each oscillator is connected to all its peers in the same community and to a subset of the oscillators in other communities. Measures are introduced for quantifying metastability, the prevalence of chimera states, and the variety of such states a system generates. By simulation, it is shown that each of these measures is maximized when the phase lag of the model is close, but not equal, to π/2. The relevance of the model to a number of fields is briefly discussed with particular emphasis on brain dynamics.

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05.45.-a

Nonlinear dynamics and chaos

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Characterization of the nontrivial and chaotic behavior that occurs in a simple city traffic model

J. Villalobos, B. A. Toledo, D. Pastén, V. Muñoz, J. Rogan, R. Zarama, N. Lammoglia, and J. A. Valdivia

Chaos 20, 013109 (2010); http://dx.doi.org/10.1063/1.3308597 (7 pages)

Online Publication Date: 4 March 2010

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We explore in detail the nontrivial and chaotic behavior of the traffic model proposed by Toledo et al. [Phys. Rev. E 70, 016107 (2004)] due to the richness of behavior present in the model, in spite of the fact that it is a minimalistic representation of basic city traffic dynamics. The chaotic behavior, previously shown for a given lower bound in acceleration/brake ratio, is examined more carefully and the region in parameter space for which we observe this nontrivial behavior is found. This parameter region may be related to the high sensitivity of traffic flow that eventually leads to traffic jams. Approximate scaling laws are proposed.

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05.45.-a

Nonlinear dynamics and chaos

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Revealing degree distribution of bursting neuron networks

Yu Shen, Zhonghuai Hou, and Houwen Xin

Chaos 20, 013110 (2010); http://dx.doi.org/10.1063/1.3300019 (5 pages)

Online Publication Date: 8 March 2010

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We present a method to infer the degree distribution of a bursting neuron network from its dynamics. Burst synchronization (BS) of coupled Morris–Lecar neurons has been studied under the weak coupling condition. In the BS state, all the neurons start and end bursting almost simultaneously, while the spikes inside the burst are incoherent among the neurons. Interestingly, we find that the spike amplitude of a given neuron shows an excellent linear relationship with its degree, which makes it possible to estimate the degree distribution of the network by simple statistics of the spike amplitudes. We demonstrate the validity of this scheme on scale-free as well as small-world networks. The underlying mechanism of such a method is also briefly discussed.

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87.19.lj

Neuronal network dynamics

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Routes to complex dynamics in a ring of unidirectionally coupled systems

P. Perlikowski, S. Yanchuk, M. Wolfrum, A. Stefanski, P. Mosiolek, and T. Kapitaniak

Chaos 20, 013111 (2010); http://dx.doi.org/10.1063/1.3293176 (10 pages) | Cited 7 times

Online Publication Date: 8 March 2010

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We study the dynamics of a ring of unidirectionally coupled autonomous Duffing oscillators. Starting from a situation where the individual oscillator without coupling has only trivial equilibrium dynamics, the coupling induces complicated transitions to periodic, quasiperiodic, chaotic, and hyperchaotic behavior. We study these transitions in detail for small and large numbers of oscillators. Particular attention is paid to the role of unstable periodic solutions for the appearance of chaotic rotating waves, spatiotemporal structures, and the Eckhaus effect for a large number of oscillators. Our analytical and numerical results are confirmed by a simple experiment based on the electronic implementation of coupled Duffing oscillators.

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05.45.Xt

Synchronization; coupled oscillators

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The existence of generalized synchronization of chaotic systems in complex networks

Aihua Hu, Zhenyuan Xu, and Liuxiao Guo

Chaos 20, 013112 (2010); http://dx.doi.org/10.1063/1.3309017 (10 pages) | Cited 2 times

Online Publication Date: 9 March 2010

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The paper studies the existence of generalized synchronization in complex networks, which consist of chaotic systems. When a part of modified nodes are chaotic, and the others have asymptotically stable equilibriums or orbital asymptotically stable periodic solutions, under certain conditions, the existence of generalized synchronization can be turned to the problem of contractive fixed point in the family of Lipschitz functions. In addition, theoretical proofs are proposed to the exponential attractive property of generalized synchronization manifold. Numerical simulations validate the theory.

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05.45.-a	Nonlinear dynamics and chaos
05.45.Xt	Synchronization; coupled oscillators

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Vibrational resonance in neuron populations

Bin Deng, Jiang Wang, Xile Wei, K. M. Tsang, and W. L. Chan

Chaos 20, 013113 (2010); http://dx.doi.org/10.1063/1.3324700 (7 pages) | Cited 11 times

Online Publication Date: 9 March 2010

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In this paper different topologies of populations of FitzHugh–Nagumo neurons have been introduce to investigate the effect of high-frequency driving on the response of neuron populations to a subthreshold low-frequency signal. We show that optimal amplitude of high-frequency driving enhances the response of neuron populations to a subthreshold low-frequency input and the optimal amplitude dependences on the connection among the neurons. By analyzing several kinds of topology (i.e., random and small world) different behaviors have been observed. Several topologies behave in an optimal way with respect to the range of low-frequency amplitude leading to an improvement in the stimulus response coherence, while others with respect to the maximum values of the performance index. However, the best results in terms of both the suitable amplitude of high-frequency driving and high stimulus response coherence have been obtained when the neurons have been connected in a small-world topology.

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89.75.Hc

Networks and genealogical trees

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Global stability analysis of birhythmicity in a self-sustained oscillator

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

Chaos 20, 013114 (2010); http://dx.doi.org/10.1063/1.3309014 (12 pages)

Online Publication Date: 9 March 2010

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We analyze the global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit-cycle variation in the van der Pol oscillator introduced to analyze enzymatic substrate reactions in brain waves. We show that the two frequencies are strongly influenced by the nonlinear coefficients α and β. With a random excitation, such as a Gaussian white noise, the attractor’s global stability is measured by the mean escape time τ from one limit cycle. An effective activation energy barrier is obtained by the slope of the linear part of the variation in the escape time τ versus the inverse noise intensity 1/D. We find that the trapping barriers of the two frequencies can be very different, thus leaving the system on the same attractor for an overwhelming time. However, we also find that the system is nearly symmetric in a narrow range of the parameters.

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05.45.Xt

Synchronization; coupled oscillators

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Function projective synchronization in chaotic and hyperchaotic systems through open-plus-closed-loop coupling

K. Sebastian Sudheer and M. Sabir

Chaos 20, 013115 (2010); http://dx.doi.org/10.1063/1.3309019 (5 pages) | Cited 6 times

Online Publication Date: 9 March 2010

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Recently introduced function projective synchronization in which chaotic systems synchronize up to a scaling function has important applications in secure communications. We design coupling function for unidirectional coupling in identical and mismatched oscillators to realize function projective synchronization through open-plus-closed-loop coupling method. Numerical simulations on Lorenz system, Rössler system, hyperchaotic Lorenz, and hyperchaotic Chen system are presented to verify the effectiveness of the proposed scheme.

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05.45.-a	Nonlinear dynamics and chaos
02.60.-x	Numerical approximation and analysis

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Multiscroll attractors by switching systems

E. Campos-Cantón, J. G. Barajas-Ramírez, G. Solís-Perales, and R. Femat

Chaos 20, 013116 (2010); http://dx.doi.org/10.1063/1.3314278 (6 pages)

Online Publication Date: 9 March 2010

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In this paper, we present a class of three-dimensional dynamical systems having multiscrolls which we call unstable dissipative systems (UDSs). The UDSs are dissipative in one of its components but unstable in the other two. This class of systems is constructed with a switching law to display various multiscroll strange attractors. The multiscroll strange attractors result from the combination of several unstable “one-spiral” trajectories by means of switching. Each of these trajectories lies around a saddle hyperbolic stationary point. Thus, we describe how a piecewise-linear switching system yields multiscroll attractors, symmetric or asymmetric, with chaotic behavior.

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05.45.Xt	Synchronization; coupled oscillators
02.30.Hq	Ordinary differential equations

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Spontaneous mode switching in coupled oscillators competing for constant amounts of resources

Yoshito Hirata, Masashi Aono, Masahiko Hara, and Kazuyuki Aihara

Chaos 20, 013117 (2010); http://dx.doi.org/10.1063/1.3329369 (7 pages) | Cited 2 times

Online Publication Date: 10 March 2010

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We propose a widely applicable scheme of coupling that models competitions among dynamical systems for fixed amounts of resources. Two oscillators coupled in this way synchronize in antiphase. Three oscillators coupled circularly show a number of oscillation modes such as rotation and partially in-phase synchronization. Intriguingly, simple oscillators in the model also produce complex behavior such as spontaneous switching among different modes. The dynamics reproduces well the spatiotemporal oscillatory behavior of a true slime mold Physarum, which is capable of computational optimization.

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05.45.Xt	Synchronization; coupled oscillators
89.75.-k	Complex systems

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Rotated balance in humans due to repetitive rotational movement

M. S. Zakynthinaki, J. Madera Milla, A. López Diaz De Durana, C. A. Cordente Martínez, G. Rodríguez Romo, M. Sillero Quintana, and J. Sampedro Molinuevo

Chaos 20, 013118 (2010); http://dx.doi.org/10.1063/1.3335460 (8 pages) | Cited 1 time

Online Publication Date: 12 March 2010

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We show how asymmetries in the movement patterns during the process of regaining balance after perturbation from quiet stance can be modeled by a set of coupled vector fields for the derivative with respect to time of the angles between the resultant ground reaction forces and the vertical in the anteroposterior and mediolateral directions. In our model, which is an adaption of the model of Stirling and Zakynthinaki (2004), the critical curve, defining the set of maximum angles one can lean to and still correct to regain balance, can be rotated and skewed so as to model the effects of a repetitive training of a rotational movement pattern. For the purposes of our study a rotation and a skew matrix is applied to the critical curve of the model. We present here a linear stability analysis of the modified model, as well as a fit of the model to experimental data of two characteristic “asymmetric” elite athletes and to a “symmetric” elite athlete for comparison. The new adapted model has many uses not just in sport but also in rehabilitation, as many work place injuries are caused by excessive repetition of unaligned and rotational movement patterns.

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87.19.rs	Movement
87.85.gj	Movement and locomotion
45.20.dc	Rotational dynamics
05.45.-a	Nonlinear dynamics and chaos

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Modeling the basin of attraction as a two-dimensional manifold from experimental data: Applications to balance in humans

Maria S. Zakynthinaki, James R. Stirling, Carlos A. Cordente Martínez, Alfonso López Díaz de Durana, Manuel Sillero Quintana, Gabriel Rodríguez Romo, and Javier Sampedro Molinuevo

Chaos 20, 013119 (2010); http://dx.doi.org/10.1063/1.3337690 (10 pages) | Cited 1 time

Online Publication Date: 12 March 2010

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We present a method of modeling the basin of attraction as a three-dimensional function describing a two-dimensional manifold on which the dynamics of the system evolves from experimental time series data. Our method is based on the density of the data set and uses numerical optimization and data modeling tools. We also show how to obtain analytic curves that describe both the contours and the boundary of the basin. Our method is applied to the problem of regaining balance after perturbation from quiet vertical stance using data of an elite athlete. Our method goes beyond the statistical description of the experimental data, providing a function that describes the shape of the basin of attraction. To test its robustness, our method has also been applied to two different data sets of a second subject and no significant differences were found between the contours of the calculated basin of attraction for the different data sets. The proposed method has many uses in a wide variety of areas, not just human balance for which there are many applications in medicine, rehabilitation, and sport.

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87.19.ru	Locomotion
87.85.gj	Movement and locomotion
87.10.-e	General theory and mathematical aspects

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Cluster synchronization in networks of coupled nonidentical dynamical systems

Wenlian Lu, Bo Liu, and Tianping Chen

Chaos 20, 013120 (2010); http://dx.doi.org/10.1063/1.3329367 (12 pages) | Cited 11 times

Online Publication Date: 17 March 2010

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In this paper, we study cluster synchronization in networks of coupled nonidentical dynamical systems. The vertices in the same cluster have the same dynamics of uncoupled node system but the uncoupled node systems in different clusters are different. We present conditions guaranteeing cluster synchronization and investigate the relation between cluster synchronization and the unweighted graph topology. We indicate that two conditions play key roles for cluster synchronization: the common intercluster coupling condition and the intracluster communication. From the latter one, we interpret the two cluster synchronization schemes by whether the edges of communication paths lie in inter- or intracluster. By this way, we classify clusters according to whether the communications between pairs of vertices in the same cluster still hold if the set of edges inter- or intracluster edges is removed. Also, we propose adaptive feedback algorithms to adapting the weights of the underlying graph, which can synchronize any bi-directed networks satisfying the conditions of common intercluster coupling and intracluster communication. We also give several numerical examples to illustrate the theoretical results.

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05.45.Xt

Synchronization; coupled oscillators

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Breakdown of invariant attractors for the dissipative standard map

Renato Calleja and Alessandra Celletti

Chaos 20, 013121 (2010); http://dx.doi.org/10.1063/1.3335408 (9 pages) | Cited 4 times

Online Publication Date: 17 March 2010

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We implement different methods for the computation of the breakdown threshold of invariant attractors in the dissipative standard mapping. A first approach is based on the computation of the Sobolev norms of the function parametrizing the solution. Then we look for the approximating periodic orbits and we analyze their stability in order to compute the critical threshold at which an invariant attractor breaks down. We also determine the domain of convergence of the dissipative standard mapping by extending the computations to the complex parameter space as well as by investigating a two-frequency model.

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05.70.Jk	Critical point phenomena
02.30.-f	Function theory, analysis

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Generalization of the JTZ model to open plane wakes

Zuo-Bing Wu

Chaos 20, 013122 (2010); http://dx.doi.org/10.1063/1.3339818 (7 pages)

Online Publication Date: 17 March 2010

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The JTZ model [ C. Jung, T. Tél, and E. Ziemniak, Chaos 3, 555 (1993) ], as a theoretical model of a plane wake behind a circular cylinder in a narrow channel at a moderate Reynolds number, has previously been employed to analyze phenomena of chaotic scattering. It is extended here to describe an open plane wake without the confined narrow channel by incorporating a double row of shedding vortices into the intermediate and far wake. The extended JTZ model is found in qualitative agreement with both direct numerical simulations and experimental results in describing streamlines and vorticity contours. To further validate its applications to particle transport processes, the interaction between small spherical particles and vortices in an extended JTZ model flow is studied. It is shown that the particle size has significant influences on the features of particle trajectories, which have two characteristic patterns: one is rotating around the vortex centers and the other accumulating in the exterior of vortices. Numerical results based on the extended JTZ model are found in qualitative agreement with experimental ones in the normal range of particle sizes.

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05.45.-a	Nonlinear dynamics and chaos
47.32.-y	Vortex dynamics; rotating fluids

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Detecting recursive and nonrecursive filters using chaos

T. L. Carroll

Chaos 20, 013123 (2010); http://dx.doi.org/10.1063/1.3357984 (9 pages)

Online Publication Date: 17 March 2010

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Filtering a chaotic signal through a recursive [or infinite impulse response (IIR)] filter has been shown to increase the dimension of chaos under certain conditions. Filtering with a nonrecursive [or finite impulse response (FIR)] filter should not increase dimension, but it has been shown that if the FIR filter has a long tail, measurements of actual signals may appear to show a dimension increase. I simulate IIR and FIR filters that correspond to naturally occurring resonant objects, and I show that using dimension measurements, I can distinguish the filter type. These measurements could be used to detect resonances using radar, sonar, or laser signals, or to determine if a resonance is due to an IIR or an FIR filter.

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