Dynamics of a delayed two-coupled oscillator with excitatory-to-excitatory connection

DOI10.1016/j.amc.2010.01.097zbMath1210.34117OpenAlexW2060702779MaRDI QIDQ963951

Shangjiang Guo, Ping Zhang, Yi-Gang He

Publication date: 14 April 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.01.097

zbMATH Keywords

stabilityoscillatordelayneural networkHopf bifurcationequilibrium

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Stability theory of functional-differential equations (34K20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18) Synchronization of solutions to ordinary differential equations (34D06)

Related Items (7)

Hopf bifurcation analysis of reaction-diffusion neural oscillator system with excitatory-to-inhibitory connection and time delay ⋮ Stability switches, bifurcation, and multi-stability of coupled networks with time delays ⋮ Multiple pitchfork bifurcations and multiperiodicity coexistences in a delay-coupled neural oscillator system with inhibitory-to-inhibitory connection ⋮ Synchronous dynamics and bifurcation analysis in two delay coupled oscillators with recurrent inhibitory loops ⋮ DYNAMICS IN TIME-DELAY RECURRENTLY COUPLED OSCILLATORS ⋮ The role of network structure and time delay in a metapopulation Wilson-Cowan model ⋮ \(Z_2 \times Z_3\) equivariant bifurcation in coupled two neural network rings

Cites Work

• Unnamed Item
• Unnamed Item
• Bifurcations, stability, and monotonicity properties of a delayed neural network model
• Amplitude response of coupled oscillators
• Synergism and antagonism of neurons caused by an electrical synapse
• Temporal dynamics of a two-neuron continuous network model with time delay
• Global existence of periodic solutions in a tri-neuron network model with delays
• Stability and bifurcation in a neural network model with two delays.
• Existence and attraction of a phase-locked oscillation in a delayed network of two neurons
• Delay induced periodicity in a neural netlet of excitation and inhibition
• Two-parameter bifurcations in a network of two neurons with multiple delays
• Regular dynamics in a delayed network of two neurons with all-or-none activation functions
• Hopf bifurcation and stability for a delayed tri-neuron network model
• Multiple pulse interactions and averaging in systems of coupled neural oscillators
• Equivariant Hopf bifurcation for neutral functional differential equations
• SHORT-TERM MEMORY AS A METASTABLE STATE. III. DIFFUSION APPROXIMATION
• Symmetric functional differential equations and neural networks with memory
• Nonlinear Waves in Networks of Neurons with Delayed Feedback: Pattern Formation and Continuation
• Stability, Bifurcation, and Multistability in a System of Two Coupled Neurons with Multiple Time Delays
• LINEAR STABILITY AND HOPF BIFURCATION IN A TWO-NEURON NETWORK WITH THREE DELAYS
• HOPF BIFURCATION OF A TWO-NEURON NETWORK WITH DIFFERENT DISCRETE TIME DELAYS
• Hopf bifurcation in the presence of symmetry

This page was built for publication: Dynamics of a delayed two-coupled oscillator with excitatory-to-excitatory connection