PATTERN FORMATION IN A RING NETWORK WITH DELAY

DOI10.1142/S0218202509004005zbMath1194.34136MaRDI QIDQ3647609

Yuan Yuan, Shangjiang Guo

Publication date: 23 November 2009

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

zbMATH Keywords

delayneural networkbifurcationnormal formcenter manifold

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Symmetries, invariants of ordinary differential equations (34C14) Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Bifurcation theory of functional-differential equations (34K18) Invariant manifolds of functional-differential equations (34K19)

Related Items (7)

Stability of synchronous slowly oscillating periodic solutions for systems of delay differential equations with coupled nonlinearity ⋮ BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY ⋮ Pattern formation of a biomass-water reaction-diffusion model ⋮ DYNAMICS IN TIME-DELAY RECURRENTLY COUPLED OSCILLATORS ⋮ Bifurcation analysis of a diffusive predator-prey system with nonmonotonic functional response ⋮ Codimension one and two bifurcations in a symmetrical ring network with delay ⋮ Oscillatory and Stationary Patterns in a Diffusive Model with Delay Effect

Cites Work

• Unnamed Item
• Unnamed Item
• Stability of nonlinear waves in a ring of neurons with delays
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Global bifurcations of phase-locked oscillators
• A simple global characterization for normal forms of singular vector fields
• Global bifurcation of periodic solutions with symmetry
• Bifurcation of zeros of parametrized functions
• The effect of time delays on the dynamics of avascular tumor growth
• Hopf bifurcating periodic orbits in a ring of neurons with delays
• A delay differential equation model for tumor growth
• Stability and synchronization of a ring of identical cells with delayed coupling
• Two-parameter bifurcations in a network of two neurons with multiple delays
• Multistability and stable asynchronous periodic oscillations in a multiple-delayed neural system
• PATTERNS OF OSCILLATION IN A RING OF IDENTICAL CELLS WITH DELAYED COUPLING
• Equivariant Hopf bifurcation for neutral functional differential equations
• ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES
• Bifurcation and symmetry breaking in applied mathematics
• Symmetric functional differential equations and neural networks with memory
• Theory and applications of Hopf bifurcations in symmetric functional differential equations
• 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
• Non-linear waves in a ring of neurons
• Neurons with graded response have collective computational properties like those of two-state neurons.
• Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling
• Hopf bifurcation in the presence of symmetry

This page was built for publication: PATTERN FORMATION IN A RING NETWORK WITH DELAY