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Dec 2008

Volume 18, Issue 4, Articles (04xxxx)

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Chaos 18, 041102 (2008); http://dx.doi.org/10.1063/1.2997332 (1 page)

Nicholas T. Ouellette and J. P. Gollub
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Announcement: Focus issue on “Intracellular Ca2+ Dynamics— A Change of Modeling Paradigm?”

Martin Falcke

Chaos 18, 040201 (2008); http://dx.doi.org/10.1063/1.2992518 (1 page)

Online Publication Date: 7 October 2008

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87.16.dp Transport, including channels, pores, and lateral diffusion
87.16.dj Dynamics and fluctuations
87.19.lp Pattern formation: activity and anatomic
87.16.Vy Ion channels
05.45.-a Nonlinear dynamics and chaos
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Introduction: Fifth Annual Gallery of Nonlinear Images (New Orleans, Louisiana, 2008)

Predrag Cvitanović, M. Cristina Marchetti, Sidney Redner, and Arshad A. Kudrolli

Chaos 18, 041101 (2008); http://dx.doi.org/10.1063/1.3052084 (1 page)

Online Publication Date: 31 December 2008

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05.45.-a Nonlinear dynamics and chaos
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Detecting topological features of chaotic fluid flow

Nicholas T. Ouellette and J. P. Gollub

Chaos 18, 041102 (2008); http://dx.doi.org/10.1063/1.2997332 (1 page)

Online Publication Date: 31 December 2008

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47.52.+j Chaos in fluid dynamics
47.55.Ca Gas/liquid flows
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Enstrophy amplification events in three-dimensional turbulence

Jörg Schumacher, Maik Boltes, Herwig Zilken, Marc-André Hermanns, Bruno Eckhardt, and Charles R. Doering

Chaos 18, 041103 (2008); http://dx.doi.org/10.1063/1.2997336 (1 page)

Online Publication Date: 31 December 2008

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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.32.-y Vortex dynamics; rotating fluids
47.11.-j Computational methods in fluid dynamics
47.27.er Spectral methods
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From bouncing to boxing

D. Terwagne, T. Gilet, N. Vandewalle, and S. Dorbolo

Chaos 18, 041104 (2008); http://dx.doi.org/10.1063/1.2997276 (1 page) | Cited 1 time

Online Publication Date: 31 December 2008

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47.55.df Breakup and coalescence
47.55.dd Bubble dynamics
47.52.+j Chaos in fluid dynamics
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Channel erosion due to subsurface flow

Braunen Smith, Arshad Kudrolli, Alexander E. Lobkovsky, and Daniel H. Rothman

Chaos 18, 041105 (2008); http://dx.doi.org/10.1063/1.2997333 (1 page)

Online Publication Date: 31 December 2008

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47.60.Dx Flows in ducts and channels
47.57.Gc Granular flow
47.56.+r Flows through porous media
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Swimming C. elegans in a wet granular medium

Sunghwan Jung, Stella Lee, and Aravinthan Samuel

Chaos 18, 041106 (2008); http://dx.doi.org/10.1063/1.2996827 (1 page)

Online Publication Date: 31 December 2008

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87.85.gj Movement and locomotion
87.19.ru Locomotion
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Force chains in a two-dimensional granular pure shear experiment

Jie Zhang, Trush Majmudar, and Robert Behringer

Chaos 18, 041107 (2008); http://dx.doi.org/10.1063/1.2997139 (1 page) | Cited 1 time

Online Publication Date: 31 December 2008

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45.70.-n Granular systems
46.25.-y Static elasticity
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Cracking sheets: Oscillatory fracture paths in thin elastic sheets

Pedro M. Reis, Basile Audoly, and Benoit Roman

Chaos 18, 041108 (2008); http://dx.doi.org/10.1063/1.2997335 (1 page)

Online Publication Date: 31 December 2008

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89.20.Kk Engineering
81.20.Wk Machining, milling
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A cascade of length scales in elastic rings under confinement

Kevin Spears and Silas Alben

Chaos 18, 041109 (2008); http://dx.doi.org/10.1063/1.2997338 (1 page)

Online Publication Date: 31 December 2008

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87.19.R- Mechanical and electrical properties of tissues and organs
87.16.Tb Mitochondria and other organelles
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Momentum distributions after double ionization

B. Eckhardt, J. Prauzner-Bechcicki, K. Sacha, and J. Zakrzewski

Chaos 18, 041110 (2008); http://dx.doi.org/10.1063/1.2997330 (1 page)

Online Publication Date: 31 December 2008

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32.80.Fb Photoionization of atoms and ions
34.80.Dp Atomic excitation and ionization
31.15.-p Calculations and mathematical techniques in atomic and molecular physics
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Inferring connectivity of interacting phase oscillators

Dongchuan Yu, Luigi Fortuna, and Fang Liu

Chaos 18, 043101 (2008); http://dx.doi.org/10.1063/1.2988279 (9 pages) | Cited 1 time

Online Publication Date: 1 October 2008

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The question as to how network topology properties influence network dynamical behavior has been extensively investigated. Here we treat the inverse problem, i.e., how to infer network connection topology from the dynamic evolution, and suggest a control based topology identification method. This method includes two steps: (i) driving the network to a steady state and (ii) inferring all elements of the connectivity matrix by exploiting information obtained from the observed steady state response of each node. We adopt different strategies for model-dependent (i.e., each local phase dynamics and coupling functions are known) and model-free (i.e., each local phase dynamics and coupling functions are unknown) cases and give detailed conditions for both cases under which network topology can be identified correctly. The influence of noise on topology identification is discussed as well. All proposed approaches are motivated and illustrated with networks of phase oscillators. We argue that these topology identification methods can be extended to general dynamical networks and are not restricted to only networks of phase oscillators.
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05.45.-a Nonlinear dynamics and chaos
02.40.Pc General topology
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Asymmetric spatiotemporal chaos induced by a polypoid mass in the excised larynx

Yu Zhang and Jack J. Jiang

Chaos 18, 043102 (2008); http://dx.doi.org/10.1063/1.2988251 (6 pages) | Cited 5 times

Online Publication Date: 7 October 2008

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In this paper, asymmetric spatiotemporal chaos induced by a polypoid mass simulating the laryngeal pathology of a vocal polyp is experimentally observed using high-speed imaging in an excised larynx. Spatiotemporal analysis reveals that the normal vocal folds show spatiotemporal correlation and symmetry. Normal vocal fold vibrations are dominated mainly by the first vibratory eigenmode. However, pathological vocal folds with a polypoid mass show broken symmetry and spatiotemporal irregularity. The spatial correlation is decreased. The pathological vocal folds spread vibratory energy across a large number of eigenmodes and induce asymmetric spatiotemporal chaos. High-order eigenmodes show complicated dynamics. Spatiotemporal analysis provides a valuable biomedical application for investigating the spatiotemporal chaotic dynamics of pathological vocal fold systems with a polypoid mass and may represent a valuable clinical tool for the detection of laryngeal mass lesion using high-speed imaging.
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43.70.Aj Anatomy and physiology of the vocal tract, speech aerodynamics, auditory kinetics
43.72.Ar Speech analysis and analysis techniques; parametric representation of speech
87.63.L- Visual imaging
87.18.Hf Spatiotemporal pattern formation in cellular populations
87.19.X- Diseases
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Winnerless competition principle and prediction of the transient dynamics in a Lotka–Volterra model

Valentin Afraimovich, Irma Tristan, Ramon Huerta, and Mikhail I. Rabinovich

Chaos 18, 043103 (2008); http://dx.doi.org/10.1063/1.2991108 (9 pages) | Cited 8 times

Online Publication Date: 8 October 2008

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Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one is interested in just asymptotic results of evolution (as time goes to infinity), then the problem has a straightforward mathematical image involving simple attractors (fixed points or limit cycles) of a dynamical system. However, for an accurate prediction of evolution, the analysis of transient solutions is critical. In this paper, in the framework of the traditional Lotka–Volterra model (generalized in some sense), we show that the transient solution representing multispecies sequential competition can be reproducible and predictable with high probability.
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05.45.-a Nonlinear dynamics and chaos
87.23.-n Ecology and evolution
02.30.Rz Integral equations
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Hopf bifurcation control in a congestion control model via dynamic delayed feedback

Songtao Guo, Gang Feng, Xiaofeng Liao, and Qun Liu

Chaos 18, 043104 (2008); http://dx.doi.org/10.1063/1.2998220 (13 pages) | Cited 3 times

Online Publication Date: 9 October 2008

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A typical objective of bifurcation control is to delay the onset of undesirable bifurcation. In this paper, the problem of Hopf bifurcation control in a second-order congestion control model is considered. In particular, a suitable Hopf bifurcation is created at a desired location with preferred properties and a dynamic delayed feedback controller is developed for the creation of the Hopf bifurcation. With this controller, one can increase the critical value of the communication delay, and thus guarantee a stationary data sending rate for larger delay. Furthermore, explicit formulae to determine the period and the direction of periodic solutions bifurcating from the equilibrium are obtained by applying perturbation approach. Finally, numerical simulation results are presented to show that the dynamic delayed feedback controller is efficient in controlling Hopf bifurcation.
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05.45.-a Nonlinear dynamics and chaos
02.60.-x Numerical approximation and analysis
07.05.Dz Control systems
02.30.Yy Control theory
02.30.Oz Bifurcation theory
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Community structures and role detection in music networks

T. Teitelbaum, P. Balenzuela, P. Cano, and Javier M. Buldú

Chaos 18, 043105 (2008); http://dx.doi.org/10.1063/1.2988285 (7 pages) | Cited 3 times

Online Publication Date: 14 October 2008

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We analyze the existence of community structures in two different social networks using data obtained from similarity and collaborative features between musical artists. Our analysis reveals some characteristic organizational patterns and provides information about the driving forces behind the growth of the networks. In the similarity network, we find a strong correlation between clusters of artists and musical genres. On the other hand, the collaboration network shows two different kinds of communities: rather small structures related to music bands and geographic zones, and much bigger communities built upon collaborative clusters with a high number of participants related through the period the artists were active. Finally, we detect the leading artists inside their corresponding communities and analyze their roles in the network by looking at a few topological properties of the nodes.
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43.75.St Musical performance, training, and analysis
05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)
01.75.+m Science and society
89.65.-s Social and economic systems
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The organization of intrinsic computation: Complexity-entropy diagrams and the diversity of natural information processing

David P. Feldman, Carl S. McTague, and James P. Crutchfield

Chaos 18, 043106 (2008); http://dx.doi.org/10.1063/1.2991106 (15 pages) | Cited 12 times

Online Publication Date: 14 October 2008

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Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display the different kinds of intrinsic computation across an entire class of systems. Here, we use complexity-entropy diagrams to analyze intrinsic computation in a broad array of deterministic nonlinear and linear stochastic processes, including maps of the interval, cellular automata, and Ising spin systems in one and two dimensions, Markov chains, and probabilistic minimal finite-state machines. Since complexity-entropy diagrams are a function only of observed configurations, they can be used to compare systems without reference to system coordinates or parameters. It has been known for some time that in special cases complexity-entropy diagrams reveal that high degrees of information processing are associated with phase transitions in the underlying process space, the so-called “edge of chaos.” Generally, though, complexity-entropy diagrams differ substantially in character, demonstrating a genuine diversity of distinct kinds of intrinsic computation.
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05.45.-a Nonlinear dynamics and chaos
02.50.Cw Probability theory
02.50.Ga Markov processes
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
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Multistability and arithmetically period-adding bifurcations in piecewise smooth dynamical systems

Younghae Do and Ying-Cheng Lai

Chaos 18, 043107 (2008); http://dx.doi.org/10.1063/1.2985853 (9 pages) | Cited 1 time

Online Publication Date: 15 October 2008

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Multistability has been a phenomenon of continuous interest in nonlinear dynamics. Most existing works so far have focused on smooth dynamical systems. Motivated by the fact that nonsmooth dynamical systems can arise commonly in realistic physical and engineering applications such as impact oscillators and switching electronic circuits, we investigate multistability in such systems. In particular, we consider a generic class of piecewise smooth dynamical systems expressed in normal form but representative of nonsmooth systems in realistic situations, and focus on the weakly dissipative regime and the Hamiltonian limit. We find that, as the Hamiltonian limit is approached, periodic attractors can be generated through a series of saddle-node bifurcations. A striking phenomenon is that the periods of the newly created attractors follow an arithmetic sequence. This has no counterpart in smooth dynamical systems. We provide physical analyses, numerical computations, and rigorous mathematical arguments to substantiate the finding.
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05.45.-a Nonlinear dynamics and chaos
02.10.Yn Matrix theory
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Dynamical parameter identification from a scalar time series

Dongchuan Yu and Fang Liu

Chaos 18, 043108 (2008); http://dx.doi.org/10.1063/1.2998550 (8 pages) | Cited 3 times

Online Publication Date: 21 October 2008

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If a drive system with unknown parameters represents “reality” and the response system a “computational model,” the unidirectional coupling can be used to change model parameters, as well as the model state, such that both systems synchronize with each other and model parameters coincide with their true values of “reality.” Such a parameter identification method is called adaptive synchronization (also autosynchronization) method and is widely used in the literature. Because one usually cannot find proper parameter update rules by exploiting information obtained from only a scalar time series, parameter identification with adaptive synchronization from a scalar time series is not well understood and still remains challenging until now. In this paper we introduce a novel adaptive synchronization approach with an effective guidance parameter to update rule design. This method includes three steps: (i) finding some proper control signals such that the “computational model” synchronizes with the “real” system if no parameter mismatch exists (that is, both systems have identical parameters); (ii) designing parameter update rules in terms of a necessary condition for ensuring local synchronization; and (iii) determining the value for each parameter update rate for ensuring the local stability of autosynchronization manifold according to the conditional Lyapunov exponents method. The reliability of the suggested technique is illustrated with the Lorenz system and a unified chaotic model.
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05.45.Xt Synchronization; coupled oscillators
05.45.Tp Time series analysis
02.50.-r Probability theory, stochastic processes, and statistics
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Synchronization-based scalability of complex clustered networks

Xiaojuan Ma, Liang Huang, Ying-Cheng Lai, Yan Wang, and Zhigang Zheng

Chaos 18, 043109 (2008); http://dx.doi.org/10.1063/1.3005782 (9 pages) | Cited 2 times

Online Publication Date: 6 November 2008

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Complex clustered networks arise in biological, social, physical, and technological systems, and the synchronous dynamics on such networks have attracted recent interests. Here we investigate system-size dependence of the synchronizability of these networks. Theoretical analysis and numerical computations reveal that, for a typical clustered network, as its size is increased, the synchronizability can be maintained or even enhanced but at the expense of deterioration of the clustered characteristics in the topology that distinguish this type of networks from other types of complex networks. An implication is that, for a large network in a realistic situation, if synchronization is important for its function, then most likely it will not have a clustered topology.
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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)
02.40.Pc General topology
89.75.Hc Networks and genealogical trees
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Cryptanalysis of a chaotic communication scheme using adaptive observer

Ying Liu and Wallace K. S. Tang

Chaos 18, 043110 (2008); http://dx.doi.org/10.1063/1.3012262 (10 pages) | Cited 1 time

Online Publication Date: 10 November 2008

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This paper addresses the cryptanalysis of a secure communication scheme recently proposed by Wu [Chaos 16, 043118 (2006) ], where the information signal is modulated into a system parameter of a unified chaotic system. With the Kerckhoff principle, assuming that the structure of the cryptosystem is known, an adaptive observer can be designed to synchronize the targeted system, so that the transmitted information and the user-specific parameters are obtained. The success of adaptive synchronization is mathematically proved with the use of Lyapunov stability theory, based on the original assumption, i.e., the dynamical evolution of the information signal is available. A more practical case, but yet much more difficult, is also considered. As demonstrated with simulations, generalized synchronization is still possible, even if the derivative of the information signal is kept secret. Hence, the message can be coarsely estimated, making the security of the considered system questionable.
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05.45.Vx Communication using chaos
05.45.Xt Synchronization; coupled oscillators
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Pinning synchronization of delayed neural networks

Jin Zhou, Xiaoqun Wu, Wenwu Yu, Michael Small, and Jun-an Lu

Chaos 18, 043111 (2008); http://dx.doi.org/10.1063/1.2995852 (9 pages) | Cited 19 times

Online Publication Date: 12 November 2008

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This paper investigates adaptive pinning synchronization of a general weighted neural network with coupling delay. Unlike recent works on pinning synchronization which proposed the possibility that synchronization can be reached by controlling only a small fraction of neurons, this paper aims to answer the following question: Which neurons should be controlled to synchronize a neural network? By using Schur complement and Lyapunov function methods, it is proved that under a mild topology-based condition, some simple adaptive feedback controllers are sufficient to globally synchronize a general delayed neural network. Moreover, for a concrete neurobiological network consisting of identical Hindmarsh–Rose neurons, a specific pinning control technique is introduced and some numerical examples are presented to verify our theoretical results.
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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)
87.85.dq Neural networks
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Synchronization of a class of chaotic systems with fully unknown parameters using adaptive sliding mode approach

M. Roopaei and M. Zolghadri Jahromi

Chaos 18, 043112 (2008); http://dx.doi.org/10.1063/1.3013601 (7 pages) | Cited 6 times

Online Publication Date: 13 November 2008

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In this paper, an adaptive sliding mode control method for synchronization of a class of chaotic systems with fully unknown parameters is introduced. In this method, no knowledge of the bounds of parameters is required in advance and the parameters are updated through an adaptive control process. We use our proposed method to synchronize two chaotic gyros, which has been the subject of intense study during the recent years for its application in the navigational, aeronautical, and space engineering domains. The effectiveness of our method is demonstrated in simulation environment and the results are compared with some recent schemes proposed in the literature for the same task.
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05.45.Gg Control of chaos, applications of chaos
05.45.Xt Synchronization; coupled oscillators
02.30.Yy Control theory
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Stability and multiple bifurcations of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity

Yongli Song, Tonghua Zhang, and Moses O. Tadé

Chaos 18, 043113 (2008); http://dx.doi.org/10.1063/1.3013195 (9 pages) | Cited 1 time

Online Publication Date: 14 November 2008

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We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov–Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved.
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05.45.-a Nonlinear dynamics and chaos
02.10.Ud Linear algebra
02.30.Oz Bifurcation theory
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On the bifurcation of species

M. A. Bees, P. H. Coullet, and E. A. Spiegel

Chaos 18, 043114 (2008); http://dx.doi.org/10.1063/1.3009196 (12 pages)

Online Publication Date: 14 November 2008

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We propose and analyze a model of evolution of species based upon a general description of phenotypes in terms of a single quantifiable characteristic. In the model, species spontaneously arise as solitary waves whose members almost never mate with those in other species, according to the rules laid down. The solitary waves in the model bifurcate and we interpret such events as speciation. Our aim in this work is to determine whether a generic mathematical mechanism may be identified with this process of speciation. Indeed, there is such a process in our model: it is the Andronov homoclinic bifurcation. It is robust and is at the heart of the formation of new solitary waves, and thus (in our model) new species.
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05.45.Yv Solitons
87.23.Kg Dynamics of evolution
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