Traveling Pulses in a Nonlocal Equation Arising Near a Saddle-Node Infinite Cycle Bifurcation

DOI10.1137/16M1093367zbMath1383.92014OpenAlexW2744118738MaRDI QIDQ5348484

Xinfu Chen, Bard Ermentrout

Publication date: 18 August 2017

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1093367

zbMATH Keywords

traveling wavesnonlocal equationsneural field

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Other nonlinear integral equations (45G10) Neural biology (92C20) Neural networks for/in biological studies, artificial life and related topics (92B20) Traveling wave solutions (35C07)

Related Items (2)

Traveling waves in non-local pulse-coupled networks ⋮ Spatiotemporal patterns in a diffusive predator–prey system with nonlocal intraspecific prey competition

Uses Software

• XPPAUT

Cites Work

• Unnamed Item
• Waves in neural media. From single neurons to neural fields
• Existence of pulses in excitable media with nonlocal coupling
• Waves in a simple, excitable or oscillatory, reaction-diffusion model
• A geometric approach to singular perturbation problems with applications to nerve impulse equations
• Dynamics of pattern formation in lateral-inhibition type neural fields
• Weakly connected neural networks
• Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations
• Waves, bumps, and patterns in neural field theories
• Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses
• Regular Traveling Waves in a One-Dimensional Network of Theta Neurons
• Existence and Stability of Traveling Pulses in a Neural Field Equation with Synaptic Depression
• Simulating, Analyzing, and Animating Dynamical Systems
• Existence and uniqueness of travelling waves for a neural network
• PDE Methods for Nonlocal Models
• NEURAL EXCITABILITY, SPIKING AND BURSTING
• Invariant manifolds

This page was built for publication: Traveling Pulses in a Nonlocal Equation Arising Near a Saddle-Node Infinite Cycle Bifurcation