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Protocol
Modeling Pacemaking, Bursting, and Depolarization Block in Midbrain Dopamine Neurons
Here we present methodology to simulate the electrical activity of neurons by using a freely available software package to numerically integrate a set of coupled nonlinear equations that describe the equival...
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Reference Work Entry In depth
Pulse-Coupled Oscillators
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Reference Work Entry In depth
Phase Response Curves: Overview
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Article
Open AccessA Mathematical Model of a Midbrain Dopamine Neuron Identifies Two Slow Variables Likely Responsible for Bursts Evoked by SK Channel Antagonists and Terminated by Depolarization Block
Midbrain dopamine neurons exhibit a novel type of bursting that we call “inverted square wave bursting” when exposed to Ca2+-activated small conductance (SK) K+ channel blockers in vitro. This type of bursting ha...
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Reference Work Entry In depth
Pulse-Coupled Oscillators
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Reference Work Entry In depth
Phase Response Curves: Overview
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Article
Open AccessEstimation of artificial neuron parameters that obtain a required distribution of coupled system periods in a hybrid network
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Living Reference Work Entry In depth
Phase Response Curves: Overview
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Article
Open AccessPerturbations can distinguish underlying dynamics in phase-locked two-neuron networks
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Article
Open AccessTheta entrainment of gamma modules: effects of heterogeneity and non-stationarity
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Article
Open AccessFixed point topology and robustness to perturbations between pairs of coupled neurons
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Chapter
History of the Application of the Phase Resetting Curve to Neurons Coupled in a Pulsatile Manner
Phase resetting curves (PRCs) keep 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. In this chapter, a history of th...
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Chapter
Phase Resetting Curve Analysis of Global Synchrony, the Splay Mode and Clustering in N Neuron all to all Pulse-Coupled Networks
We use phase resetting curve (PRC) theory to analyze phase-locked patterns in pulse-coupled all to all network of N neurons that receive multiple inputs per cycle. The basic principles are that the phase must be ...
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Article
Responses of a bursting pacemaker to excitation reveal spatial segregation between bursting and spiking mechanisms
Central pattern generators (CPGs) frequently include bursting neurons that serve as pacemakers for rhythm generation. Phase resetting curves (PRCs) can provide insight into mechanisms underlying phase locking ...
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Article
Effects of conduction delays on the existence and stability of one to one phase locking between two pulse-coupled oscillators
Gamma oscillations can synchronize with near zero phase lag over multiple cortical regions and between hemispheres, and between two distal sites in hippocampal slices. How synchronization can take place over l...
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Article
Open AccessPhase locking and resetting in human subthalamic neurons
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Article
Open AccessThe role of ERG current in pacemaking and bursting in dopamine neurons
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Article
Stability of two cluster solutions in pulse coupled networks of neural oscillators
Phase response curves (PRCs) have been widely used to study synchronization in neural circuits comprised of pacemaking neurons. They describe how the timing of the next spike in a given spontaneously firing ne...
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Article
Synaptic and intrinsic determinants of the phase resetting curve for weak coupling
A phase resetting curve (PRC) keeps track of the extent to which a perturbation at a given phase advances or delays the next spike, and can be used to predict phase locking in networks of oscillators. The PRC ...
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Article
Open AccessMutually pulse-coupled neurons that do not synchronize in isolation can synchronize via reciprocal coupling with another neural population