41 citations · 239 across the 19 of their papers we have counts for
18 papers · 1 filter
Symmetry-Breaking Bifurcations for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities in 2-D
Merlin Pelz, Michael J. Ward
For a 2-D coupled PDE-ODE bulk-cell model, we investigate symmetry-breaking bifurcations that can emerge when two bulk diffusing species are coupled to two-component nonlinear intr…
A ring of spikes
Theodore Kolokolnikov, Michael Ward
For the Schnakenberg model, we consider a highly symmetric configuration of N spikes whose locations are located at the vertices of a regular N-gon inside either a unit disk or an…
An Asymptotic Analysis of Localized 3-D Spot Patterns for Gierer-Meinhardt Model: Existence, Linear Stability and Slow Dynamics
Daniel Gomez, Michael J. Ward, Juncheng Wei
Localized spot patterns, where one or more solution components concentrates at certain points in the domain, are a common class of localized pattern for reaction-diffusion systems,…
Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Sensing with Small Signaling Compartments
Sarafa A. Iyaniwura, Michael J. Ward
We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized…
Localized Signaling Compartments in 2-D Coupled by a Bulk Diffusion Field: Quorum Sensing and Synchronous Oscillations in the Well-Mixed Limit
Sarafa A. Iyaniwura, Michael J. Ward
We analyze oscillatory instabilities for a coupled PDE-ODE system modeling the communication between localized spatially segregated dynamically active signaling compartments that a…
Stable Asymmetric Spike Equilibria for the Gierer-Meinhardt Model with a Precursor Field
Theodore Kolokolnikov, Frédéric Paquin-Lefebvre, Michael J. Ward
Precursor gradients in a reaction-diffusion system are spatially varying coefficients in the reaction-kinetics. Such gradients have been used in various applications, such as the h…