ReviewMathematical biosciences2010
Pulse coupled oscillators and the phase resetting curve.
Review in Mathematical biosciences, 2010. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 25 papers.
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Who cites it
25 citing papers in PubMed.
- A mean field theory for pulse-coupled neural oscillators based on the spike time response curve.Journal of neurophysiology · 2025Article
- Existence and stability criteria for global synchrony and for synchrony in two alternating clusters of pulse-coupled oscillators updated to include conduction delays.Mathematical biosciences · 2024Article
- Optimal synchronization in pulse-coupled oscillator networks using reinforcement learning.PNAS nexus · 2023Article
- Article
- Interneuronal network model of theta-nested fast oscillations predicts differential effects of heterogeneity, gap junctions and short term depression for hyperpolarizing versus shunting inhibition.PLoS computational biology · 2022Article
- Phase response approaches to neural activity models with distributed delay.Biological cybernetics · 2022Review
- Differential contributions of synaptic and intrinsic inhibitory currents to speech segmentation via flexible phase-locking in neural oscillators.PLoS computational biology · 2021Article
- First-order synchronization transition in a large population of strongly coupled relaxation oscillators.Science advances · 2020Article
- Phase response theory explains cluster formation in sparsely but strongly connected inhibitory neural networks and effects of jitter due to sparse connectivity.Journal of neurophysiology · 2019Article
- Response of an oscillatory differential delay equation to a single stimulus.Journal of mathematical biology · 2017Article
- Globally attracting synchrony in a network of oscillators with all-to-all inhibitory pulse coupling.Physical review. E · 2017Article
- Neurons as oscillators.Journal of neurophysiology · 2016Review
- Stimulus-dependent synchronization in delayed-coupled neuronal networks.Scientific reports · 2016Article
- Slow noise in the period of a biological oscillator underlies gradual trends and abrupt transitions in phasic relationships in hybrid neural networks.PLoS computational biology · 2014Article
- Statistical analysis of the pulse-coupled synchronization strategy for wireless sensor networks.IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society · 2013Article
- Phase resetting reduces theta-gamma rhythmic interaction to a one-dimensional map.Journal of mathematical biology · 2013Article
- Effect of phase response curve skew on synchronization with and without conduction delays.Frontiers in neural circuits · 2013Article
- Optimal phase response functions for fast pulse-coupled synchronization in wireless sensor networks.IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society · 2012Article
- Energy-efficient pulse-coupled synchronization strategy design for wireless sensor networks through reduced idle listening.IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society · 2012Article
- Short conduction delays cause inhibition rather than excitation to favor synchrony in hybrid neuronal networks of the entorhinal cortex.PLoS computational biology · 2012Article
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2 authors.
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Abstract
Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.