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Synchronization of pulsecoupled biological oscillators
 SIAM J. Appl. Math
, 1990
"... Abstract. A simple model for synchronous firing of biological oscillators based on Peskin’s model of ..."
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Abstract. A simple model for synchronous firing of biological oscillators based on Peskin’s model of
On the Stability of the Kuramoto Model of Coupled Nonlinear Oscillators
, 2005
"... We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for alltoall networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using ..."
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Cited by 62 (8 self)
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We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for alltoall networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value, the synchronized state is locally asymptotically stable, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We further explain the behavior of the system as the number of oscillators grows to infinity.
Exploring Synchronization in Complex Oscillator Networks
"... Abstract — The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator network is characterized by a population of hetero ..."
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Abstract — The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing the interaction among the oscillators. These two ingredients give rise to a rich dynamic behavior that keeps on fascinating the scientific community. In this article, we present a tutorial introduction to coupled oscillator networks, we review the vast literature on theory and applications, and we present a collection of different synchronization notions, conditions, and analysis approaches. We focus on the canonical phase oscillator models occurring in countless realworld synchronization phenomena, and present their rich phenomenology. We review a set of applications relevant to control scientists. We explore different approaches to phase and frequency synchronization, and we present a collection of synchronization conditions and performance estimates. For all results we present selfcontained proofs that illustrate a sample of different analysis methods in a tutorial style. I.
Synchronization of clocks
"... Abstract: In this report we recall the famous Huygens ’ experiment which gave the first evidence of the synchronization phenomenon. We consider the synchronization of two clocks which are accurate (show the same time) but have pendulawith different masses. It has been shown that such clocks hanging ..."
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Abstract: In this report we recall the famous Huygens ’ experiment which gave the first evidence of the synchronization phenomenon. We consider the synchronization of two clocks which are accurate (show the same time) but have pendulawith different masses. It has been shown that such clocks hanging on the same beam can show the almost complete (inphase) and almost antiphase synchronizations. By almost complete and almost antiphase synchronization we defined the periodic motion of the pendula in which the phase shift between the displacements of the pendula is respectively close (but not equal) to 0 or π.We give evidence that almost antiphase synchronization was the phenomenon observed by Huygens in XVII century. We support our numerical studies by considering the energy balance in the system and showing how the energy is transferred between the pendula via oscillating beam allowing the pendula’s synchronization. Additionally we discuss the synchronization of a number of different pendulum clocks hanging from a horizontal beam which can roll on the parallel surface. It has been shown that after a transient, different types of synchronization between pendula can be observed;(i) the complete synchronization in which all pendula behave identically, (ii) pendula create three or five clusters of synchronized pendula. We derive the equations for the estimation of the phase differences between phase synchronized clusters. The evidence, why other configurations with a different number of clusters are not observed, is given. *Corresponding author.
AND
, 909
"... A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and numerically that finitesize systems may have many different synchr ..."
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A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and numerically that finitesize systems may have many different synchronized stable solutions which are characterised by different values of the winding number. The lower bound for the critical coupling kc is given, as well as an algorithm for its exact calculation. It is shown that in general phaselocking does not lead to phase coherence in 1D. PACS numbers: 05.45.Xt 1.
A SynchronyBased Perspective for Partner Selection and Attentional Mechanism in HumanRobot Interaction
, 2013
"... Future robots must coexist and directly interact with human beings. Designing these agents imply solving hard problems linked to humanrobot interaction tasks. For instance, how a robot can choose an interacting partner among various agents and how a robot locates regions of interest in its visual ..."
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Future robots must coexist and directly interact with human beings. Designing these agents imply solving hard problems linked to humanrobot interaction tasks. For instance, how a robot can choose an interacting partner among various agents and how a robot locates regions of interest in its visual field. Studies of neurobiology and psychology
Rotation sets for networks of circle maps
, 2005
"... We consider continuous maps of the torus, homotopic to the identity, that arise from systems of coupled circle maps and discuss the relationship between network architecture and rotation sets. Our main result is that when the map on the torus is invertible, network architecture can force the set of ..."
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We consider continuous maps of the torus, homotopic to the identity, that arise from systems of coupled circle maps and discuss the relationship between network architecture and rotation sets. Our main result is that when the map on the torus is invertible, network architecture can force the set of rotation vectors to lie in a lowdimensional subspace. In particular, the rotation set for an alltoall coupled system of identical cells must be a subset of a line. 1
Synchronization inComplexNetworksof PhaseOscillators:ASurvey
"... The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in realworl ..."
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The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in realworld synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finitedimensional and infinitedimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research. 1
SYNCHRONIZATION OF ASYMPTOTICALLY PERIODIC BEHAVIORS IN COUNTABLE CELLULAR SYSTEMS
"... We address the question of frequencies locking in coupled differential systems and of the existence of (component) quasiperiodic solutions of some kind of differential systems. These systems named “cellular systems”,are quite general as they deal with countable number of coupled systems in some gen ..."
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We address the question of frequencies locking in coupled differential systems and of the existence of (component) quasiperiodic solutions of some kind of differential systems. These systems named “cellular systems”,are quite general as they deal with countable number of coupled systems in some general Banach spaces. Moreover, the inner dynamics of each subsystem does not have to be specified. We reach some general results about how the frequencies locking phenomenon is related to the structure of the coupling map, and therefore about the localization of a certain type of quasiperiodic solutions of differential systems that may be seen as cellular systems. This paper gives some explanations about how and why synchronized behaviors naturally occur in a wide variety of complex systems. Keywords. Coupled systems, synchronization, frequencies locking, quasiperiodic motions, differential systems, asymptotically periodic. 1