Complete dynamical analysis of a neuron model
type: Item
instance of: scholarly article
title: Complete dynamical analysis of a neuron model
zbMATH Open document ID: 1254.37058
published in: Nonlinear Dynamics
publication date: 2013-01-04T00:00:00Z
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92C20
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 34K60
zbMATH DE Number: 6122191
zbMATH Keywords: neuron model
zbMATH Keywords: bifurcation
zbMATH Keywords: bursting
zbMATH Keywords: bistability
zbMATH Keywords: Poincaré mapping
zbMATH Keywords: parameter continuation
zbMATH Keywords: complex dynamics
author: Andrey Shilnikov
MaRDI profile type: Publication
full work available at URL: s11071-011-0046-y
OpenAlex ID: W2152707060
cites work: Topological and phenomenological classification of bursting oscillations
cites work: Multirhythmic bursting
cites work: Q3710353
cites work: Q4863262
cites work: NEURAL EXCITABILITY, SPIKING AND BURSTING
cites work: Q5796192
cites work: Q3275127
cites work: Geometric singular perturbation theory for ordinary differential equations
cites work: Q4866649
cites work: Tracking invariant manifolds with differential forms in singularly perturbed systems
cites work: The transition from bursting to continuous spiking in excitable membrane models
cites work: From simple to complex oscillatory behaviour via intermittent chaos in the Rose-Hindmarsh model for neuronal activity
cites work: Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle
cites work: Homoclinic bifurcation in a Hodgkin–Huxley model of thermally sensitive neurons
cites work: Food chain chaos due to Shilnikov’s orbit
cites work: Subthreshold oscillations in a map-based neuron model
cites work: Q4264342
cites work: Q4947577
cites work: Q3371991
cites work: Chaos in a three-variable model of an excitable cell
cites work: ORIGIN OF CHAOS IN A TWO-DIMENSIONAL MAP MODELING SPIKING-BURSTING NEURAL ACTIVITY
cites work: Reduction of a model of an excitable cell to a one-dimensional map
cites work: Return Map Characterizations for a Model of Bursting with Two Slow Variables
cites work: Voltage interval mappings for activity transitions in neuron models for elliptic bursters
cites work: On bifurcations of the Lorenz attractor in the Shimizu-Morioka model
cites work: Homoclinic bifurcations of periodic orbits on a route from tonic spiking to bursting in neuron models
cites work: Ghostbursting: the effects of dendrites on spike patterns
cites work: GLOBAL TANGENCY AND TRANSVERSALITY OF PERIODIC FLOWS AND CHAOS IN A PERIODICALLY FORCED, DAMPED DUFFING OSCILLATOR
cites work: Q4519409
cites work: Q3051125
cites work: ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. I
cites work: Q4337943
cites work: Q3782469
cites work: Q4381995
cites work: SMOOTH SYMMETRIC AND LORENZ MODELS FOR UNIMODAL MAPS
cites work: Period Three Implies Chaos
cites work: Blue sky catastrophes
cites work: Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model
cites work: Spontaneous voltage oscillations and response dynamics of a Hodgkin-Huxley type model of sensory hair cells
DOI: 10.1007/S11071-011-0046-Y
description: scientific article; zbMATH DE number 6122191