Phase diagram for the Winfree model of coupled nonlinear oscillators.
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The first bifurcation analysis of the Winfree mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators is given, for a tractable special case.Abstract:
In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.read more
Citations
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Journal ArticleDOI
The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Journal ArticleDOI
Synchronization in complex networks
Alex Arenas,Alex Arenas,Albert Díaz-Guilera,Albert Díaz-Guilera,Jürgen Kurths,Jürgen Kurths,Yamir Moreno,Changsong Zhou +7 more
TL;DR: The advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology are reported and the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections are overviewed.
Journal ArticleDOI
The Kuramoto model: A simple paradigm for synchronization phenomena
TL;DR: In this paper, a review of the Kuramoto model of coupled phase oscillators is presented, with a rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years.
Journal ArticleDOI
Effects of noise in excitable systems
Benjamin Lindner,Jordi Garcia-Ojalvo,Jordi Garcia-Ojalvo,Alexander Neiman,Alexander Neiman,Lutz Schimansky-Geier,Lutz Schimansky-Geier +6 more
TL;DR: In this article, the behavior of excitable systems driven by Gaussian white noise is reviewed, focusing mainly on those general properties of such systems that are due to noise, and present several applications of their findings in biophysics and lasers.
Journal ArticleDOI
Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience
TL;DR: In this article, a set of mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understand network dynamics in neuroscience.
References
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Journal ArticleDOI
The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Book
The geometry of biological time
TL;DR: The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways is presented.
Journal ArticleDOI
Synchronization of pulse-coupled biological oscillators
TL;DR: A simple model for synchronous firing of biological oscillators based on Peskin's model of the cardiac pacemaker is studied in this article, which consists of a population of identical integrate-and-fire oscillators, whose coupling between oscillators is pulsatile: when a given oscillator fires, it pulls the others up by a fixed amount, or brings them to the firing threshold, whichever is less.
Journal ArticleDOI
Biological rhythms and the behavior of populations of coupled oscillators
TL;DR: It is proposed that self-entraining communities of this sort may exist within individual metazoan animals and plants as the basis of the observed diurnal coordination of their physiological process.