Lyapunov exponents computation for hybrid neurons.

Abstract:

:Lyapunov exponents are a basic and powerful tool to characterise the long-term behaviour of dynamical systems. The computation of Lyapunov exponents for continuous time dynamical systems is straightforward whenever they are ruled by vector fields that are sufficiently smooth to admit a variational model. Hybrid neurons do not belong to this wide class of systems since they are intrinsically non-smooth owing to the impact and sometimes switching model used to describe the integrate-and-fire (I&F) mechanism. In this paper we show how a variational model can be defined also for this class of neurons by resorting to saltation matrices. This extension allows the computation of Lyapunov exponent spectrum of hybrid neurons and of networks made up of them through a standard numerical approach even in the case of neurons firing synchronously.

journal_name

J Comput Neurosci

authors

Bizzarri F,Brambilla A,Gajani GS

doi

10.1007/s10827-013-0448-6

subject

Has Abstract

pub_date

2013-10-01 00:00:00

pages

201-12

issue

2

eissn

0929-5313

issn

1573-6873

journal_volume

35

pub_type

杂志文章
  • System identification of Drosophila olfactory sensory neurons.

    abstract::The lack of a deeper understanding of how olfactory sensory neurons (OSNs) encode odors has hindered the progress in understanding the olfactory signal processing in higher brain centers. Here we employ methods of system identification to investigate the encoding of time-varying odor stimuli and their representation f...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-010-0265-0

    authors: Kim AJ,Lazar AA,Slutskiy YB

    更新日期:2011-02-01 00:00:00

  • Calcium control of triphasic hippocampal STDP.

    abstract::Synaptic plasticity is believed to represent the neural correlate of mammalian learning and memory function. It has been demonstrated that changes in synaptic conductance can be induced by approximately synchronous pairings of pre- and post- synaptic action potentials delivered at low frequencies. It has also been est...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-012-0397-5

    authors: Bush D,Jin Y

    更新日期:2012-12-01 00:00:00

  • From stimulus estimation to combination sensitivity: encoding and processing of amplitude and timing information in parallel, convergent sensory pathways.

    abstract::Information theoretical approaches to sensory processing in electric fish have focused on the encoding of amplitude modulations in a single sensory pathway in the South American gymnotiforms. To assess the generality of these studies, we investigated the encoding of amplitude and phase modulations in the distantly rel...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-007-0062-6

    authors: Carlson BA,Kawasaki M

    更新日期:2008-08-01 00:00:00

  • A minimum-error, energy-constrained neural code is an instantaneous-rate code.

    abstract::Sensory neurons code information about stimuli in their sequence of action potentials (spikes). Intuitively, the spikes should represent stimuli with high fidelity. However, generating and propagating spikes is a metabolically expensive process. It is therefore likely that neural codes have been selected to balance en...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-016-0592-x

    authors: Johnson EC,Jones DL,Ratnam R

    更新日期:2016-04-01 00:00:00

  • Two-cell to N-cell heterogeneous, inhibitory networks: precise linking of multistable and coherent properties.

    abstract::Inhibitory networks are now recognized as being the controllers of several brain rhythms. However, experimental work with inhibitory cells is technically difficult not only because of their smaller percentage of the neuronal population, but also because of their diverse properties. As such, inhibitory network models w...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-005-0331-1

    authors: Skinner FK,Bazzazi H,Campbell SA

    更新日期:2005-06-01 00:00:00

  • State-dependent effects of Na channel noise on neuronal burst generation.

    abstract::We explore the effects of stochastic sodium (Na) channel activation on the variability and dynamics of spiking and bursting in a model neuron. The complete model segregates Hodgin-Huxley-type currents into two compartments, and undergoes applied current-dependent bifurcations between regimes of periodic bursting, chao...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1023/B:JCNS.0000014104.08299.8b

    authors: Rowat PF,Elson RC

    更新日期:2004-03-01 00:00:00

  • Reduced order models of myelinated axonal compartments.

    abstract::The paper presents a hierarchical series of computational models for myelinated axonal compartments. Three classes of models are considered, either with distributed parameters (2.5D EQS-ElectroQuasi Static, 1D TL-Transmission Lines) or with lumped parameters (0D). They are systematically analyzed with both analytical ...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-019-00726-4

    authors: Ioan D,Bărbulescu R,Silveira LM,Ciuprina G

    更新日期:2019-12-01 00:00:00

  • Modeling mesoscopic cortical dynamics using a mean-field model of conductance-based networks of adaptive exponential integrate-and-fire neurons.

    abstract::Voltage-sensitive dye imaging (VSDi) has revealed fundamental properties of neocortical processing at macroscopic scales. Since for each pixel VSDi signals report the average membrane potential over hundreds of neurons, it seems natural to use a mean-field formalism to model such signals. Here, we present a mean-field...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-017-0668-2

    authors: Zerlaut Y,Chemla S,Chavane F,Destexhe A

    更新日期:2018-02-01 00:00:00

  • Model analyses of visual biofeedback training for EEG-based brain-computer interface.

    abstract::The primary goal of this study was to construct a simulation model of a biofeedback brain-computer interface (BCI) system to analyze the effect of biofeedback training on BCI users. A mathematical model of a man-machine visual-biofeedback BCI system was constructed to simulate a subject using a BCI system to control c...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-009-0148-4

    authors: Chen CW,Ju MS,Sun YN,Lin CC

    更新日期:2009-12-01 00:00:00

  • ModelDB: A Database to Support Computational Neuroscience.

    abstract::Wider dissemination and testing of computational models are crucial to the field of computational neuroscience. Databases are being developed to meet this need. ModelDB is a web-accessible database for convenient entry, retrieval, and running of published models on different platforms. This article provides a guide to...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1023/B:JCNS.0000023869.22017.2e

    authors: Hines ML,Morse T,Migliore M,Carnevale NT,Shepherd GM

    更新日期:2004-07-01 00:00:00

  • A common goodness-of-fit framework for neural population models using marked point process time-rescaling.

    abstract::A critical component of any statistical modeling procedure is the ability to assess the goodness-of-fit between a model and observed data. For spike train models of individual neurons, many goodness-of-fit measures rely on the time-rescaling theorem and assess model quality using rescaled spike times. Recently, there ...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-018-0698-4

    authors: Tao L,Weber KE,Arai K,Eden UT

    更新日期:2018-10-01 00:00:00

  • Relating reflex gain modulation in posture control to underlying neural network properties using a neuromusculoskeletal model.

    abstract::During posture control, reflexive feedback allows humans to efficiently compensate for unpredictable mechanical disturbances. Although reflexes are involuntary, humans can adapt their reflexive settings to the characteristics of the disturbances. Reflex modulation is commonly studied by determining reflex gains: a set...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-010-0278-8

    authors: Schuurmans J,van der Helm FC,Schouten AC

    更新日期:2011-06-01 00:00:00

  • Spiking neural network simulation: numerical integration with the Parker-Sochacki method.

    abstract::Mathematical neuronal models are normally expressed using differential equations. The Parker-Sochacki method is a new technique for the numerical integration of differential equations applicable to many neuronal models. Using this method, the solution order can be adapted according to the local conditions at each time...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-008-0131-5

    authors: Stewart RD,Bair W

    更新日期:2009-08-01 00:00:00

  • Comparative power spectral analysis of simultaneous electroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media : EEG and MEG power spectra.

    abstract::The resistive or non-resistive nature of the extracellular space in the brain is still debated, and is an important issue for correctly modeling extracellular potentials. Here, we first show theoretically that if the medium is resistive, the frequency scaling should be the same for electroencephalogram (EEG) and magne...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-010-0252-5

    authors: Dehghani N,Bédard C,Cash SS,Halgren E,Destexhe A

    更新日期:2010-06-17 00:00:00

  • Testing for significance of phase synchronisation dynamics in the EEG.

    abstract::A number of tests exist to check for statistical significance of phase synchronisation within the Electroencephalogram (EEG); however, the majority suffer from a lack of generality and applicability. They may also fail to account for temporal dynamics in the phase synchronisation, regarding synchronisation as a consta...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-012-0428-2

    authors: Daly I,Sweeney-Reed CM,Nasuto SJ

    更新日期:2013-06-01 00:00:00

  • From global to local: exploring the relationship between parameters and behaviors in models of electrical excitability.

    abstract::Models of electrical activity in excitable cells involve nonlinear interactions between many ionic currents. Changing parameters in these models can produce a variety of activity patterns with sometimes unexpected effects. Further more, introducing new currents will have different effects depending on the initial para...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-016-0600-1

    authors: Fletcher P,Bertram R,Tabak J

    更新日期:2016-06-01 00:00:00

  • Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents.

    abstract::Many neuron types exhibit preferred frequency responses in their voltage amplitude (resonance) or phase shift to subthreshold oscillatory currents, but the effect of biophysical parameters on these properties is not well understood. We propose a general framework to analyze the role of different ionic currents and the...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-013-0483-3

    authors: Rotstein HG,Nadim F

    更新日期:2014-08-01 00:00:00

  • A simple model of human foveal ganglion cell responses to hyperacuity stimuli.

    abstract::We developed a physiologically plausible model of the first steps of spatial visual information processing in the fovea of the human retina. With the predictions of this model we could support the hypothesis that, for moderate contracts (< or = 40%), hyperacuity is mediated by the magnocellular (MC-) pathway. Despite ...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/BF00158338

    authors: Wachtler T,Wehrhahn C,Lee BB

    更新日期:1996-03-01 00:00:00

  • Crossover inhibition in the retina: circuitry that compensates for nonlinear rectifying synaptic transmission.

    abstract::In the mammalian retina, complementary ON and OFF visual streams are formed at the bipolar cell dendrites, then carried to amacrine and ganglion cells via nonlinear excitatory synapses from bipolar cells. Bipolar, amacrine and ganglion cells also receive a nonlinear inhibitory input from amacrine cells. The most commo...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-009-0170-6

    authors: Molnar A,Hsueh HA,Roska B,Werblin FS

    更新日期:2009-12-01 00:00:00

  • Correction to: Psychophysical detection and learning in freely behaving rats: a probabilistic dynamical model for operant conditioning.

    abstract::The original version of this article unfortunately has some typographical errors in equations (5), (6), (7), (8), and (12). ...

    journal_title:Journal of computational neuroscience

    pub_type: 已发布勘误

    doi:10.1007/s10827-020-00759-0

    authors: Devecioğlu İ,Güçlü B

    更新日期:2020-08-01 00:00:00

  • Model of familiarity discrimination in the perirhinal cortex.

    abstract::Much evidence indicates that recognition memory involves two separable processes, recollection and familiarity discrimination, with familiarity discrimination being dependent on the perirhinal cortex of the temporal lobe. Here, we describe a new neural network model designed to mimic the response patterns of perirhina...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1023/a:1008925909305

    authors: Bogacz R,Brown MW,Giraud-Carrier C

    更新日期:2001-01-01 00:00:00

  • Improved dimensionally-reduced visual cortical network using stochastic noise modeling.

    abstract::In this paper, we extend our framework for constructing low-dimensional dynamical system models of large-scale neuronal networks of mammalian primary visual cortex. Our dimensional reduction procedure consists of performing a suitable linear change of variables and then systematically truncating the new set of equatio...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-011-0359-3

    authors: Tao L,Praissman J,Sornborger AT

    更新日期:2012-04-01 00:00:00

  • Computational principles underlying the recognition of acoustic signals in insects.

    abstract::Many animals produce pulse-like signals during acoustic communication. These signals exhibit structure on two time scales: they consist of trains of pulses that are often broadcast in packets-so called chirps. Temporal parameters of the pulse and of the chirp are decisive for female preference. Despite these signals b...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-013-0441-0

    authors: Clemens J,Hennig RM

    更新日期:2013-08-01 00:00:00

  • Spatiotemporal maps of CaMKII in dendritic spines.

    abstract::The calcium calmodulin dependent kinase (CaMKII) is important for long-term potentiation at dendritic spines. Photo-activatable GFP (PaGFP) - CaMKII fusions were used to map CaMKII movements between and within spines in dissociated hippocampal neurons. Photo-activated PaGFP (GFP*) generated in the shaft spread uniform...

    journal_title:Journal of computational neuroscience

    pub_type: 历史文章,杂志文章

    doi:10.1007/s10827-011-0377-1

    authors: Khan S,Reese TS,Rajpoot N,Shabbir A

    更新日期:2012-08-01 00:00:00

  • Evolution and analysis of model CPGs for walking: I. Dynamical modules.

    abstract::Can one develop an abstract description of the dynamics of pattern generators that provides quantitative insight into their operation? We explored this question by examining the dynamics of a model central pattern generator that was created using an evolutionary algorithm. We propose an abstract description based on t...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1023/a:1008923704408

    authors: Chiel HJ,Beer RD,Gallagher JC

    更新日期:1999-09-01 00:00:00

  • No parallel fiber volleys in the cerebellar cortex: evidence from cross-correlation analysis between Purkinje cells in a computer model and in recordings from anesthetized rats.

    abstract::Purkinje cells aligned on the medio-lateral axis share a large proportion of their approximately 175,000 parallel fiber inputs. This arrangement has led to the hypothesis that movement timing is coded in the cerebellum by beams of synchronously active parallel fibers. In computer simulations I show that such synchrono...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1023/a:1023217111784

    authors: Jaeger D

    更新日期:2003-05-01 00:00:00

  • The effect of morphology upon electrophysiological responses of retinal ganglion cells: simulation results.

    abstract::Retinal ganglion cells (RGCs) display differences in their morphology and intrinsic electrophysiology. The goal of this study is to characterize the ionic currents that explain the behavior of ON and OFF RGCs and to explore if all morphological types of RGCs exhibit the phenomena described in electrophysiological data...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-013-0463-7

    authors: Maturana MI,Kameneva T,Burkitt AN,Meffin H,Grayden DB

    更新日期:2014-04-01 00:00:00

  • Effects of conduction delays on the existence and stability of one to one phase locking between two pulse-coupled oscillators.

    abstract::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 long distances in a stable manner is considered an open question. The phase resetting curve (PRC) keeps track o...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-011-0315-2

    authors: Woodman MM,Canavier CC

    更新日期:2011-10-01 00:00:00

  • A continuous attractor network model without recurrent excitation: maintenance and integration in the head direction cell system.

    abstract::Motivated by experimental observations of the head direction system, we study a three population network model that operates as a continuous attractor network. This network is able to store in a short-term memory an angular variable (the head direction) as a spatial profile of activity across neurons in the absence of...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/s10827-005-6559-y

    authors: Boucheny C,Brunel N,Arleo A

    更新日期:2005-03-01 00:00:00

  • Modeling Hermissenda: I. Differential contributions of IA and IC to type-B cell plasticity.

    abstract::We developed a multicompartmental Hodgkin-Huxley model of the Hermissenda type-B photoreceptor and used it to address the relative contributions of reductions of two K+ currents, IA and IC, to changes in cellular excitability and synaptic strength that occur in these cells after associative learning. We found that red...

    journal_title:Journal of computational neuroscience

    pub_type: 杂志文章

    doi:10.1007/BF00160809

    authors: Fost JW,Clark GA

    更新日期:1996-06-01 00:00:00