Hopf-pitchfork bifurcation in a two-neuron system with discrete and distributed delays

DOI10.1002/mma.3418zbMath1334.92027OpenAlexW1768958976MaRDI QIDQ2795264

Jingnan Wang, Hongbin Wang

Publication date: 18 March 2016

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.3418

zbMATH Keywords

stabilitydelayperiodic orbitneuron systemHopf-pitchfork bifurcation

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Bifurcations of singular points in dynamical systems (37G10) Bifurcation theory of functional-differential equations (34K18)

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Cites Work

• Unnamed Item
• Hopf-zero bifurcation in a generalized Gopalsamy neural network model
• On the coexistence of periodic or quasi-periodic oscillations near a Hopf-pitchfork bifurcation in NFDE
• Hopf bifurcation and stability for a neural network model with mixed delays
• Hopf-transcritical bifurcation in retarded functional differential equations
• Hopf and Bogdanov-Takens bifurcations in a coupled FitzHugh-Nagumo neural system with delay
• Dynamics in three cells with multiple time delays
• Hopf-pitchfork bifurcation in van der Pol's oscillator with nonlinear delayed feedback
• Multiple Hopf bifurcations of symmetric BAM neural network model with delay
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Applications of centre manifold theory
• Stability in asymmetric Hopfield nets with transmission delays
• On a planar system modelling a neuron network with memory
• Global existence of periodic solutions in a tri-neuron network model with delays
• Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays
• Stability and bifurcation in a neural network model with two delays.
• Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain
• Dynamics of a two-neuron system with discrete and distributed delays
• Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
• Codimension two bifurcation in a delayed neural network with unidirectional coupling
• On the use of small training sets for neural network-based characterization of mixed pixels in remotely sensed hyperspectral images
• Hopf bifurcation control for delayed complex networks
• Two-parameter bifurcations in a network of two neurons with multiple delays
• Pattern memory analysis based on stability theory of cellular neural networks
• FOLD–HOPF BIFURCATION ANALYSIS FOR A COUPLED FITZHUGH–NAGUMO NEURAL SYSTEM WITH TIME DELAY
• AN EFFICIENT METHOD FOR STUDYING FOLD-HOPF BIFURCATION IN DELAYED NEURAL NETWORKS
• Absolute stability of global pattern formation and parallel memory storage by competitive neural networks
• QUALITATIVE ANALYSIS OF A NEURAL NETWORK MODEL WITH MULTIPLE TIME DELAYS
• New conditions for global stability of neural networks with application to linear and quadratic programming problems
• Neurons with graded response have collective computational properties like those of two-state neurons.