Search results for "Biological neuron model"

showing 5 items of 5 documents

Simulations of the cultured granule neuron excitability

2003

Abstract We have developed a biophysical model of a cultured rat cerebellar granule neuron and simulated its excitability under different experimental conditions. The basic excitability properties of such a small neuron; the specific action potential waveforms, the overall firing patterns induced by current stimulations, and the linear frequency-current relation, are the main model constraints. Simulations show that for a one-compartmental granule neuron model, the constraints are met using six voltage- and time-dependent ion channel types and calcium dynamics linked to BK Ca ion channel function. This kind of model of a single neuron forms a solid basis for building the increasingly more c…

CerebellumQuantitative Biology::Neurons and CognitionChemistryCognitive NeuroscienceBiological neuron modelSmall neuronComputer Science Applicationsmedicine.anatomical_structureGranular cellnervous systemArtificial IntelligenceCalcium dynamicsmedicineBiological neural networkNeuronNeuroscienceIon channelNeurocomputing
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Active spike transmission in the neuron model with a winding threshold manifold

2012

International audience; We analyze spiking responses of excitable neuron model with a winding threshold manifold on a pulse stimulation. The model is stimulated with external pulse stimuli and can generate nonlinear integrate-and-fire and resonant responses typical for excitable neuronal cells (all-or-none). In addition we show that for certain parameter range there is a possibility to trigger a spiking sequence with a finite number of spikes (a spiking message) in the response on a short stimulus pulse. So active transformation of N incoming pulses to M (with M>N) outgoing spikes is possible. At the level of single neuron computations such property can provide an active "spike source" comp…

Cognitive Neuroscience[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][ NLIN.NLIN-CD ] Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD]Threshold manifoldBiological neuron modelMachine learningcomputer.software_genreTopology01 natural sciences010305 fluids & plasmaslaw.inventionSpike encodingArtificial Intelligencelaw0103 physical sciences010306 general physicsSpike transmissionActive responseBifurcationMathematicsExcitabilityQuantitative Biology::Neurons and Cognitionbusiness.industry[SCCO.NEUR]Cognitive science/NeuroscienceDissipationComputer Science ApplicationsPulse (physics)[SPI.TRON]Engineering Sciences [physics]/Electronics[ SPI.TRON ] Engineering Sciences [physics]/ElectronicsNonlinear systemTransmission (telecommunications)Nonlinear dynamics[NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD][ SCCO.NEUR ] Cognitive science/NeuroscienceSpike (software development)Artificial intelligencebusinessManifold (fluid mechanics)computer
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Periodic and Chaotic Orbits of a Neuron Model

2015

In this paper we study a class of difference equations which describes a discrete version of a single neuron model. We consider a generalization of the original McCulloch-Pitts model that has two thresholds. Periodic orbits are investigated accordingly to the different range of parameters. For some parameters sufficient conditions for periodic orbits of arbitrary periods have been obtained. We conclude that there exist values of parameters such that the function in the model has chaotic orbits. Models with chaotic orbits are not predictable in long-term.

Discrete mathematicsQuantitative Biology::Neurons and CognitionGeneralizationMathematical analysisChaoticBiological neuron modelFunction (mathematics)stabilityDynamical systemStability (probability)dynamical systemModeling and Simulationiterative processRange (statistics)Orbit (dynamics)QA1-939chaotic mappingnonlinear problemAnalysisMathematicsMathematicsMathematical Modelling and Analysis
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Eventually periodic solutions of single neuron model

2020

In this paper, we consider a nonautonomous piecewise linear difference equation that describes a discrete version of a single neuron model with a periodic (period two and period three) internal decay rate. We investigated the periodic behavior of solutions relative to the periodic internal decay rate in our previous papers. Our goal is to prove that this model contains a large quantity of initial conditions that generate eventually periodic solutions. We will show that only periodic solutions and eventually periodic solutions exist in several cases.

Period (periodic table)Differential equationApplied Mathematics010102 general mathematicsMathematical analysisperiodic solutionlcsh:QA299.6-433difference equationBiological neuron modellcsh:Analysis01 natural sciencesneuron model010101 applied mathematicsPiecewise linear functioneventually periodic solution0101 mathematicsAnalysisMathematicsNonlinear Analysis: Modelling and Control
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Periodic orbits of a neuron model with periodic internal decay rate

2015

In this paper we will study a non-autonomous piecewise linear difference equation which describes a discrete version of a single neuron model with a periodic internal decay rate. We will investigate the periodic behavior of solutions relative to the periodic internal decay rate. Furthermore, we will show that only periodic orbits of even periods can exist and show their stability character.

Piecewise linear functionComputational MathematicsCharacter (mathematics)Classical mechanicsDifferential equationApplied MathematicsMathematical analysisPeriodic orbitsPeriodic sequenceBiological neuron modelStability (probability)MathematicsApplied Mathematics and Computation
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