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Quadratization: From conductance-based models to caricature models with parabolic nonlinearities

https://doi.org/10.1101/137422
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/978-0-387-87708-2openalex-snapshot
Mathematical Foundations of Neuroscience
inferredcites →https://doi.org/10.1007/978-1-4614-0739-3_3openalex-snapshot
A Theoretical Framework for the Dynamics of Multiple Intrinsic Oscillators in Single Neurons
inferredcites →https://doi.org/10.1007/s10827-006-8096-8openalex-snapshot
The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells
inferredcites →https://doi.org/10.1007/s10827-014-0544-2openalex-snapshot
Subthreshold amplitude and phase resonance in models of quadratic type: Nonlinear effects generated by the interplay of resonant and amplifying currents
inferredcites →https://doi.org/10.1007/s10827-016-0632-6openalex-snapshot
The shaping of intrinsic membrane potential oscillations: positive/negative feedback, ionic resonance/amplification, nonlinearities and time scales
inferredcites →https://doi.org/10.1007/s10827-017-0661-9openalex-snapshot
Spiking resonances in models with the same slow resonant and fast amplifying currents but different subthreshold dynamic properties
inferredcites →https://doi.org/10.1016/s0893-6080(01)00078-8openalex-snapshot
Resonate-and-fire neurons
inferredcites →https://doi.org/10.1016/s1472-9288(01)00012-7openalex-snapshot
A firing-rate model of spike-frequency adaptation in sinusoidally-driven thalamocortical relay neurons
inferredcites →https://doi.org/10.1017/cbo9781107447615openalex-snapshot
Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition
inferredcites →https://doi.org/10.1023/a:1024474819512openalex-snapshot
Synchronization of Strongly Coupled Excitatory Neurons: Relating Network Behavior to Biophysics
inferredcites →https://doi.org/10.1038/nn1352openalex-snapshot
Similar network activity from disparate circuit parameters
inferredcites →https://doi.org/10.1063/1.4824320openalex-snapshot
Abrupt and gradual transitions between low and hyperexcited firing frequencies in neuronal models with fast synaptic excitation: A comparative study
inferredcites →https://doi.org/10.1093/oso/9780195104912.001.0001openalex-snapshot
Biophysics of Computation
inferredcites →https://doi.org/10.1098/rsta.2010.0130openalex-snapshot
Hybrid spiking models
inferredcites →https://doi.org/10.1103/physrevlett.86.4175openalex-snapshot
Existence and Stability of Persistent States in Large Neuronal Networks
inferredcites →https://doi.org/10.1109/tnn.2003.820440openalex-snapshot
Simple model of spiking neurons
inferredcites →https://doi.org/10.1113/jphysiol.1952.sp004764openalex-snapshot
A quantitative description of membrane current and its application to conduction and excitation in nerve
inferredcites →https://doi.org/10.1137/070687268openalex-snapshot
Bifurcation Analysis of a General Class of Nonlinear Integrate-and-Fire Neurons
inferredcites →https://doi.org/10.1137/100809866openalex-snapshot
Canard-Like Explosion of Limit Cycles in Two-Dimensional Piecewise-Linear Models of FitzHugh–Nagumo Type
inferredcites →https://doi.org/10.1137/s0036141099360919openalex-snapshot
Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
inferredcites →https://doi.org/10.1152/jn.00357.2016openalex-snapshot
Dynamic compensation mechanism gives rise to period and duty-cycle level sets in oscillatory neuronal models
inferredcites →https://doi.org/10.1152/jn.00686.2005openalex-snapshot
Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity
inferredcites →https://doi.org/10.1152/jn.00955.2002openalex-snapshot
From Subthreshold to Firing-Rate Resonance
inferredcites →https://doi.org/10.1152/jn.01116.2003openalex-snapshot
Subthreshold Resonance Explains the Frequency-Dependent Integration of Periodic as Well as Random Stimuli in the Entorhinal Cortex
inferredcites →https://doi.org/10.1152/jn.2000.83.2.808openalex-snapshot
Intrinsic Dynamics in Neuronal Networks. I. Theory
inferredcites →https://doi.org/10.1186/2190-8567-4-11openalex-snapshot
Frequency Preference Response to Oscillatory Inputs in Two-dimensional Neural Models: A Geometric Approach to Subthreshold Amplitude and Phase Resonance
inferredcites →https://doi.org/10.1523/eneuro.0018-15.2015openalex-snapshot
Competing Mechanisms of Gamma and Beta Oscillations in the Olfactory Bulb Based on Multimodal Inhibition of Mitral Cells Over a Respiratory Cycle
inferredcites →https://doi.org/10.1523/jneurosci.23-37-11628.2003openalex-snapshot
How Spike Generation Mechanisms Determine the Neuronal Response to Fluctuating Inputs
inferredcites →https://doi.org/10.1523/jneurosci.2601-15.2015openalex-snapshot
Resonant Interneurons Can Increase Robustness of Gamma Oscillations
inferredcites →https://doi.org/10.7551/mitpress/2526.001.0001openalex-snapshot
Dynamical Systems in Neuroscience

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/s00422-019-00802-zopenalex-snapshot
Frequency-dependent responses of neuronal models to oscillatory inputs in current versus voltage clamp
inferred← citeshttps://doi.org/10.1007/s10827-025-00908-3openalex-snapshot
Postsynaptic frequency filters shaped by the interplay of synaptic short-term plasticity and cellular time scales
inferred← citeshttps://doi.org/10.1101/2025.09.12.675827openalex-snapshot
Frequency-dependent coupling in response to oscillatory inputs in networks of electrically coupled nodes: Gap junction networks and spatially extended neurons - Full Version
inferred← citeshttps://doi.org/10.1101/515510openalex-snapshot
Frequency dependent responses of neuronal models to oscillatory inputs in current versus voltage clamp
inferred← citeshttps://doi.org/10.1162/neco_a_01680openalex-snapshot
Pulse Shape and Voltage-Dependent Synchronization in Spiking Neuron Networks
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