Stability and bifurcation of a two-neuron network with distributed time delays

DOI10.1016/j.nonrwa.2009.03.004zbMath1205.34106OpenAlexW1983401781MaRDI QIDQ974561

Cheng-Hsiung Hsu, Tzi-Sheng Yang, Suh-Yuh Yang, Ting-Hui Yang

Publication date: 3 June 2010

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2009.03.004

zbMATH Keywords

neural networklocal stabilityHopf bifurcationdistributed time delaypitchfork bifurcation

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Stability theory of functional-differential equations (34K20) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18) Invariant manifolds of functional-differential equations (34K19)

Related Items

Stability and bifurcation analysis for a neural network model with discrete and distributed delays

Uses Software

• Time-Delay System Toolbox

Cites Work

• Unnamed Item
• Bifurcations, stability, and monotonicity properties of a delayed neural network model
• Nonlinear dynamics and stability of analog neural networks
• Introduction to functional differential equations
• Stability in asymmetric Hopfield nets with transmission delays
• Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays
• On the exponential stability and periodic solutions of delayed cellular neural networks
• Existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients.
• Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
• Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
• Delay induced periodicity in a neural netlet of excitation and inhibition
• Almost Kenmotsu 3−h -manifolds with cyclic-parallel Ricci tensor
• ON PERIODIC SOLUTIONS OF A TWO-NEURON NETWORK SYSTEM WITH SIGMOIDAL ACTIVATION FUNCTIONS
• Stability, Bifurcation, and Multistability in a System of Two Coupled Neurons with Multiple Time Delays
• Frustration, Stability, and Delay-Induced Oscillations in a Neural Network Model
• Neurons with graded response have collective computational properties like those of two-state neurons.