The bifurcation study of 1:2 resonance in a delayed system of two coupled neurons
type: Item
instance of: scholarly article
title: The bifurcation study of 1:2 resonance in a delayed system of two coupled neurons
zbMATH Open document ID: 1279.34084
author: Guihong Fan
author: Sue Ann Campbell
author: Gail S. K. Wolkowicz
author: Huanping Zhu
published in: Journal of Dynamics and Differential Equations
publication date: 2013-05-06T00:00:00Z
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K19
Mathematics Subject Classification ID: 34K17
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92B20
zbMATH DE Number: 6160876
zbMATH Keywords: delay
zbMATH Keywords: 1:2 resonance
zbMATH Keywords: Bogdanov-Takens bifurcation
zbMATH Keywords: center manifold
zbMATH Keywords: normal form
zbMATH Keywords: universal unfolding
zbMATH Keywords: neuron
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: homoclinic orbit
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: s10884-012-9279-9
OpenAlex ID: W1976081455
cites work: Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
cites work: Stability and Bifurcations of Equilibria in a Multiple-Delayed Differential Equation
cites work: Q3667656
cites work: Q3667657
cites work: Q4867267
cites work: Frustration, Stability, and Delay-Induced Oscillations in a Neural Network Model
cites work: Q4225186
cites work: Zero singularities of codimension two and three in delay differential equations
cites work: Q4305607
cites work: Q5296665
cites work: Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Delay induced periodicity in a neural netlet of excitation and inhibition
cites work: Neurons with graded response have collective computational properties like those of two-state neurons.
cites work: Introduction to functional differential equations
cites work: Symbolic computation for center manifolds and normal forms of Bogdanov bifurcation in retarded functional differential equations
cites work: Elements of applied bifurcation theory.
cites work: Stability of functional differential equations
cites work: Bifurcations, stability, and monotonicity properties of a delayed neural network model
cites work: Effect of Delay on the Boundary of the Basin of Attraction in a Self-Excited Single Graded-Response Neuron
cites work: Q4715203
cites work: Stability, Bifurcation, and Multistability in a System of Two Coupled Neurons with Multiple Time Delays
cites work: Forced oscillations and bifurcations
DOI: 10.1007/S10884-012-9279-9
Recommended article: Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain
Recommended article: Bifurcation analysis of a two-neuron system with distributed delays
Recommended article: The Bogdanov-Takens bifurcation study of \(2m\) coupled neurons system with \(2m+1\) delays
Recommended article: Bifurcation structure of two coupled FHN neurons with delay
Recommended article: Two-parameter bifurcations in a network of two neurons with multiple delays
Recommended article: Bifurcation analysis on a two-neuron system with distributed delays
Recommended article: Stability, Bifurcation, and Multistability in a System of Two Coupled Neurons with Multiple Time Delays
Recommended article: Hopf bifurcation analysis of coupled two-neuron system with discrete and distributed delays
Recommended article: Hopf-pitchfork bifurcation in a two-neuron system with discrete and distributed delays
Recommended article: Stability and bifurcation in a discrete system of two neurons with delays
description: scientific article; zbMATH DE number 6160876