2019
DOI: 10.1088/1751-8121/ab0b4c
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The Winfree model with heterogeneous phase-response curves: analytical results

Abstract: We study an extension of the Winfree model of coupled phase oscillators in which both natural frequencies and phase-response curves (PRCs) are heterogeneous. In the first part of the paper we resort to averaging and derive an approximate model, in which the oscillators are coupled through their phase differences. Remarkably, this simplified model is the 'Kuramoto model with distributed shear' (2011 Phys. Rev. Lett. 106 254101). We find that above a critical level of PRC heterogeneity the incoherent state is al… Show more

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Cited by 11 publications
(10 citation statements)
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“…At the same time, our findings are consistent with an in vitro study of how intrinsic heterogeneity in the phase response curve (PRC) characteristics of olfactory bulb mitral cells limits correlationinduced synchronous neural oscillations (Burton et al, 2012). See also the theoretical analysis of Pazó et al (2019), which finds that beyond a critical level of PRC heterogeneity, the incoherent state-a simple equilibrium-is always stable. These works, and our observations reported here, suggest that evolution tunes the diversity of neuronal populations to achieve an appropriate balance between dynamical complexity and simplicity, depending on function.…”
Section: Discussionsupporting
confidence: 87%
See 1 more Smart Citation
“…At the same time, our findings are consistent with an in vitro study of how intrinsic heterogeneity in the phase response curve (PRC) characteristics of olfactory bulb mitral cells limits correlationinduced synchronous neural oscillations (Burton et al, 2012). See also the theoretical analysis of Pazó et al (2019), which finds that beyond a critical level of PRC heterogeneity, the incoherent state-a simple equilibrium-is always stable. These works, and our observations reported here, suggest that evolution tunes the diversity of neuronal populations to achieve an appropriate balance between dynamical complexity and simplicity, depending on function.…”
Section: Discussionsupporting
confidence: 87%
“…However, fast-spiking neurons are typically inhibitory, and regularly-spiking neurons are typically excitatory, suggesting that it would be interesting to analyze our network with a more complicated joint probability distribution g(η, k). Fifth, Pazó and Montbrió (2014) applied the OA technique to study pulse-coupled oscillators described by phase response curves, an approach that makes it possible to study the role of synaptic diversity in networks of Type II neurons (Pazó et al, 2019). Sixth, previous work has shown that in populations of coupled excitable systems subjected to an external periodic driving and/or noise, a resonance effect can occur for an optimal degree of oscillator diversity (Tessone et al, 2006(Tessone et al, , 2007.…”
Section: Discussionmentioning
confidence: 99%
“…Similar multiheaded chimera states were previously only observed in laser systems [11,12]. Due to the inherent heterogeneity in periods and phase response behavior [40], the oscillators in the clusters show a larger phase spread than in simulations with homogeneous oscillators. Stronger heterogeneity can furthermore lead to phase switchers [41], which prevent the formation of stationary clusters, resulting in an apparently incoherent domain.…”
Section: Methodssupporting
confidence: 77%
“…One of the first models for interacting oscillators was the Winfree model (Winfree, 1967 ; Ariaratnam and Strogatz, 2001 ; Pazó and Montbrió, 2014 ; Ha et al, 2015 ; Gallego et al, 2017 ; Pazó et al, 2019 ; Pazó and Gallego, 2020 ). Each Winfree oscillator is described by a single angular variable and when uncoupled is assumed to undergo periodic oscillations.…”
Section: Introductionmentioning
confidence: 99%