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Broad Range of Neural Dynamics From a Time-Varying FitzHugh–Nagumo Model and its Spiking Threshold Estimation

R. T. Faghih, K. Savla, M. A. Dahleh, E. N. Brown
2012 IEEE Transactions on Biomedical Engineering  
We demonstrate the use of the FHN model from an estimation perspective by presenting a novel parameter estimation method that exploits its multiple time-scale properties, and compare the performance of  ...  We study the use of the FitzHugh-Nagumo (FHN) model for capturing neural spiking. The FHN model is a widely used approximation of the Hodgkin-Huxley model that has significant limitations.  ...  Hodgkin-Huxley (HH), Hindmarsh-Rose (HR) [18] , and FitzHugh-Nagumo (FHN) [8] , [14] models are among the most successful dynamical models in computational neuroscience for capturing neural spiking  ... 
doi:10.1109/tbme.2011.2180020 pmid:22186931 fatcat:piwmtwn6jjco5hzesltjm4bp2m

Fractal ion-channel behavior generates fractal firing patterns in neuronal models

Steven B. Lowen, Larry S. Liebovitch, John A. White
1999 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Here, we examine the effects of fractal ion-channel activity in modifications of two classical neuronal models: Fitzhugh-Nagumo ͑FHN͒ and Hodgkin-Huxley ͑HH͒.  ...  Fractal behavior has been observed in both ion-channel gating and neuronal spiking patterns, but a causal relationship between the two has not yet been established.  ...  During the time between one spike and the next the membrane voltage assumes a wide range of values, which in turn generates a time-varying power-law exponent for the ion channels.  ... 
doi:10.1103/physreve.59.5970 pmid:11969579 fatcat:zr7vmdclobfufd2onbzaaqsrh4

A closer look at the apparent correlation of structural and functional connectivity in excitable neural networks

Arnaud Messé, Marc-Thorsten Hütt, Peter König, Claus C. Hilgetag
2015 Scientific Reports  
of a neural network, in particular its modularity.  ...  We compared the results obtained by the SER model with corresponding simulations by another well established dynamic mechanism, the Fitzhugh-Nagumo model, in order to explore general features of the SC-FC  ...  MTH acknowledges support from DFG grant HU 937/7. PK is supported by DFG grants SFB 936/ B6 and ERC-2010-AdG #269716. CCH is supported by DFG grants HI 1286/5-1 and SFB 936/A1.  ... 
doi:10.1038/srep07870 pmid:25598302 pmcid:PMC4297952 fatcat:imrnkkprg5hpxde4q2htd4cqru

Noise-induced synchronization and anti-resonance in excitable systems; Implications for information processing in Parkinson's Disease and Deep Brain Stimulation [article]

Jonathan D. Touboul, Charlotte Piette, Laurent Venance, G. Bard Ermentrout
2019 arXiv   pre-print
models of neuronal networks.  ...  Indeed, for noise and coupling within specific ranges, an asymmetry in the transition rates between a resting and an excited regime progressively builds up, leading to an increase in the fraction of excited  ...  Section I introduces our reference neural network model, the electrically coupled FitzHugh-Nagumo network, and describes numerically the emergence of the noise-induced synchronization in this model.  ... 
arXiv:1905.01342v2 fatcat:h6xxykkvqnfvzokxpuf3mmko2i

How we hear what is not there: A neural mechanism for the missing fundamental illusion

Dante R. Chialvo
2003 Chaos  
A nonlinear model is proposed here in which a noisy detection produces neural spikes, occurring at a rate identical to the perceived pitch for the complex tone.  ...  This phenomenon exemplifies a larger variety of problems related to how pitch is extracted from complex tones, music and speech, and thus has been extensively used to test theories of pitch perception.  ...  A Visiting Professorship from the Physics Department of Universitat de les Illes Balears, Mallorca, Spain ͑summer of 2003͒ and the support from the Veterans Administrations GLAHS and the NIH are also recognized  ... 
doi:10.1063/1.1617771 pmid:14604413 fatcat:i2a5xrqztnguxbmmthwrdjrtm4

Dynamical Instability Determines the Effect of Ongoing Noise on Neural Firing

David E. O'Gorman, John A. White, Christopher A. Shera
2009 Journal of the Association for Research in Otolaryngology  
We demonstrate, however, that the nonlinear dynamics of neural excitation and refractoriness embodied in the FitzHugh-Nagumo (FN) model produce realistic firing irregularity at high stimulus rates, even  ...  This instability, quantified by the value of the Lyapunov exponent, may play a critical role in determining modulation sensitivity and dynamic range in cochlear implants.  ...  Grants This work was supported by a Speech and Hearing Science Training Grant from the NIDCD (T32-DC00038), the Kirschstein Award (NIH F31-DC006188), an MIT-Poitras Fellowship, and the MIT-Zakhartchenko  ... 
doi:10.1007/s10162-008-0148-5 pmid:19308644 pmcid:PMC2674196 fatcat:lp5z2owrmrbjxmujfpekurh7zi

Coherence Resonance in Coupled Theta Neurons

Woochang Woochang, Sang-Yoon Sang-Yoon, Sunae Sunae
2007 Journal of the Korean Physical Society  
For the coupled case, each local neuron may be driven by a temporally coherent synaptic current occurring due to spatial coherence between neural spikings.  ...  We study the temporal coherence resonance (CR) of a local neuron in an excitatory network of globally coupled canonical type-I theta neurons.  ...  ., the FitzHugh-Nagumo model [2] , the Plant model and the Hindmarsh-Rose model [3] , and the Hodgkin-Huxley model [6] ).  ... 
doi:10.3938/jkps.50.219 fatcat:shgb3mod65hx3a4opu75sr6eyu

Modelling the perception of music in brain network dynamics [article]

Jakub Sawicki, Lenz Hartmann, Rolf Bader, Eckehard Schöll
2022 arXiv   pre-print
We analyze the influence of music in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in healthy human subjects.  ...  We report an increase of coherence between the global dynamics in our network and the input signal induced by a specific music song.  ...  ACKNOWLEDGMENTS We are grateful to Antonín Škoch and Jaroslav Hlinka for preparing the example structural connectivity matrices.  ... 
arXiv:2204.00562v2 fatcat:oem5r6uqd5drhlulbajdyz7n2a

Delayed correlations improve the reconstruction of the brain connectome

Mite Mijalkov, Joana B. Pereira, Giovanni Volpe, Nuno Araujo
2020 PLoS ONE  
This approach relies on the assumption that the activation of connected regions occurs together and at the same time.  ...  We obtain similar results in networks derived from animal and human data.  ...  Second, we use the Fitzhugh-Nagumo model of spiking neurons (Methods "Fitzhugh-Nagumo model") [44, 45] .  ... 
doi:10.1371/journal.pone.0228334 pmid:32074115 pmcid:PMC7029855 fatcat:ehaiploxqjh6beue72el7fx374

Threshold Firing Frequency–Current Relationships of Neurons in Rat Somatosensory Cortex: Type 1 and Type 2 Dynamics

T. Tateno, A. Harsch, H. P. C. Robinson
2004 Journal of Neurophysiology  
Neurons and dynamical models of spike generation display two different types of threshold behavior, with steady current stimulation: type 1 [the firing frequency vs. current ( f-I) relationship is continuous  ...  at a frequency that varied smoothly over a large range as stimulus intensity varied, whereas others were relatively insensitive to stimulus intensity (Hodgkin 1948).  ...  These models have 6 and 4 dynamical variables, respectively, but the essence of type 1 and type 2 behavior may be understood with 2 variables, as in the FitzHugh-Nagumo (FitzHugh 1961; Nagumo et al. 1962  ... 
doi:10.1152/jn.00109.2004 pmid:15381746 fatcat:h3fjds3i6zdbfh2vwbpshkuk2y

Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm

Joshua Chang, David Paydarfar
2014 Journal of Computational Neuroscience  
We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradientbased algorithm: 1) enables automated exploration of a wide solution space, using  ...  Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior.  ...  This work was supported by NIH R01 GM104987 and the Wyss Institute of Biologically Inspired Engineering.  ... 
doi:10.1007/s10827-014-0525-5 pmid:25145955 pmcid:PMC4225195 fatcat:r2vpzqsg55ehta2r635hslk7em

Emergence of Resonances in Neural Systems: The Interplay between Adaptive Threshold and Short-Term Synaptic Plasticity

Jorge F. Mejias, Joaquin J. Torres, Vladimir Brezina
2011 PLoS ONE  
Our main results are confirmed by employing a more realistic FitzHugh-Nagumo neuron model, which displays threshold variability, as well as by considering more realistic stochastic synaptic models and  ...  In this work we study the detection of weak stimuli by spiking (integrate-and-fire) neurons in the presence of certain level of noisy background neural activity.  ...  Lugo and J. Faubert for providing useful data, J. Marro for a critical reading of the manuscript, and Pablo Varona for useful discussions and advice. Author Contributions  ... 
doi:10.1371/journal.pone.0017255 pmid:21408148 pmcid:PMC3050837 fatcat:oqiartlfsbfidhg7fd7am354su

Dynamical structures in binary media of potassium-driven neurons

D. E. Postnov, F. Müller, R. B. Schuppner, L. Schimansky-Geier
2009 Physical Review E  
We address this problem by studying simplified excitable units given by a modified FitzHugh-Nagumo dynamics.  ...  In the spatially extended situation various patterns appear ranging from spirals and traveling waves to oscillons and inverted structures depending on the parameters of the medium.  ...  Using the FitzHugh-Nagumo model as prototype for an excitable unit, we added a pathway that qualitatively takes into account the potassium release from the neurons and the depolarization (threshold lowering  ... 
doi:10.1103/physreve.80.031921 pmid:19905160 fatcat:23dxtd44lvbq3mrfubt2emqp4y

Data-driven discovery of governing equations for coarse-grained heterogeneous network dynamics [article]

Katherine Owens, J. Nathan Kutz
2022 arXiv   pre-print
We then apply the mathematical framework to discovering low-dimensional dynamics in networks of semi-synchronized Kuramoto, Rayleigh, Rossler, and Fitzhugh-Nagumo oscillators, as well as heterogeneous  ...  We also provide a numerical exploration of the dimension of collective network dynamics as a function of several network parameters, showing that the discovery of coarse-grained variables and dynamics  ...  Acknowledgements The authors acknowledge funding support from the Air Force Office of Scientific Research (AFOSR FA9550-19-1-0386) and from the National Science Foundation AI Institute in Dynamic Systems  ... 
arXiv:2205.10965v1 fatcat:kbdvvubktndnrgk67fkq5hrhje

Synaptic input sequence discrimination on behavioral timescales mediated by reaction-diffusion chemistry in dendrites

Upinder Singh Bhalla
2017 eLife  
We suggest that this mechanism provides highly parallel and selective neural computation in a functionally important time range.  ...  We predict that dendritic sequence-recognition zones occupy 5 to 30 microns and recognize time-intervals of 0.2 to 5 s.  ...  The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.  ... 
doi:10.7554/elife.25827 pmid:28422010 pmcid:PMC5426902 fatcat:zdi5xxk6h5hl5l6rjnsn7miv3i
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