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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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Cited by 190 (0 self)
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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
 In Proceedings of the American Control Conference
, 2004
"... We provide a complete analysis of the Kuramoto model of coupled nonlinear oscillators with uncertain natural frequencies and arbitrary interconnection topology. Our work extends and supersedes existing, partial results for the case of an alltoall connected network. Using tools from spectral gra ..."
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Cited by 58 (8 self)
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We provide a complete analysis of the Kuramoto model of coupled nonlinear oscillators with uncertain natural frequencies and arbitrary interconnection topology. Our work extends and supersedes existing, partial results for the case of an alltoall connected network. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value all the oscillators synchronize, resulting in convergence of all phase di#erences 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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Cited by 1 (1 self)
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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.
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
FREQUENCY LOCKING IN TISSULAR COUPLING
"... Abstract. We expose a framework, inspired by biological observations, dedicated to modeling complex living systems as coupled systems. In particular, we use this framework to adress a main question in the field of living systems: the synchronization phenomenon. This kind of model, named tissular cou ..."
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Abstract. We expose a framework, inspired by biological observations, dedicated to modeling complex living systems as coupled systems. In particular, we use this framework to adress a main question in the field of living systems: the synchronization phenomenon. This kind of model, named tissular coupling, is quite general and, using different methods from those usually used in this field of research, we reach global results relative to the frequencies locking problem in both finite and continuous populations.
FREQUENCY LOCKING IN COUNTABLE CELLULAR SYSTEMS, LOCALIZATION OF (ASYMPTOTIC) QUASIPERIODIC SOLUTIONS OF AUTONOMOUS DIFFERENTIAL SYSTEMS ∗
"... Abstract. We address the question of frequency locking in coupled differential systems and of the existence of some quasiperiodic solutions of a certain kind of differential systems. Those systems are named “cellular systems ” quite generally as they deal with countable numbers of coupled systems i ..."
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Abstract. We address the question of frequency locking in coupled differential systems and of the existence of some quasiperiodic solutions of a certain kind of differential systems. Those systems are named “cellular systems ” quite generally as they deal with countable numbers 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 frequency locking phenomenon is related to the structure of the coupling map. Those results can be restated in terms of localization of a certain type of quasiperiodic solution 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.
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