Oscillatory Dynamics for a Coupled Membrane-Bulk Diffusion Model with Fitzhugh--Nagumo Membrane Kinetics

DOI10.1137/15M1028297zbMath1347.35032MaRDI QIDQ2799044

Michael J. Ward, Jia Gou

Publication date: 8 April 2016

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

zbMATH Keywords

Hopf bifurcationwinding numbersynchronous oscillationsactive membranesbulk diffusionslow-fast membrane dynamics

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Perturbations in context of PDEs (35B20) Bifurcations in context of PDEs (35B32) Semilinear parabolic equations (35K58) Biological rhythms and synchronization (92B25) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (11)

An asymptotic analysis of a 2-D model of dynamically active compartments coupled by bulk diffusion ⋮ Synchronized Oscillatory Dynamics for a 1-D Model of Membrane Kinetics Coupled by Linear Bulk Diffusion ⋮ Dynamically active compartments coupled by a stochastically gated gap junction ⋮ A theory of synchrony by coupling through a diffusive chemical signal ⋮ Weakly Nonlinear Theory for Oscillatory Dynamics in a One-Dimensional PDE-ODE Model of Membrane Dynamics Coupled by a Bulk Diffusion Field ⋮ A theory of synchrony for active compartments with delays coupled through bulk diffusion ⋮ Dynamics of epidemic spreading on connected graphs ⋮ A PDE-DDE Model for Cell Polarization in Fission Yeast ⋮ Synchronous oscillations for a coupled cell-bulk ODE-PDE model with localized cells on \({\mathbb{R}}^2\) ⋮ Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Mediated Communication between Small Signaling Compartments ⋮ Pattern Formation and Oscillatory Dynamics in a Two-Dimensional Coupled Bulk-Surface Reaction-Diffusion System

Uses Software

• XPPAUT

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