2 citations · 2 across the 7 of their papers we have counts for
7 papers
Dynamical behavior of diffusively coupled scalar differential equations as Wentzell boundary conditions
Merlin Pelz
Two identical scalar dynamical systems coupled through a scalar diffusion equation are studied herein, with respect to bifurcations from a symmetric steady-state to symmetric and a…
Oscillations in a scalar differential equation coupled to a diffusive field
Merlin Pelz, Arnd Scheel
We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quan…
Compartmental-reaction diffusion framework for microscale dynamics of extracellular serotonin in brain tissue
Merlin Pelz, Skirmantas Janusonis, Gregory Handy
Serotonin (5-hydroxytryptamine) is a major neurotransmitter whose release from densely distributed serotonergic varicosities shapes plasticity and network integration throughout th…
Synchronized Memory-Dependent Intracellular Oscillations for a Cell-Bulk ODE-PDE Model in
Merlin Pelz, Michael J. Ward
For a cell-bulk ODE-PDE model in , a hybrid asymptotic-numerical theory is developed to provide a new theoretical and computationally efficient approach for studying…
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…
The Emergence of Spatial Patterns for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities
Merlin Pelz, Michael J. Ward
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemi…
A PIC method with Forward-Backward Lagrangian reconstructions
Martin Campos Pinto, Merlin Pelz, Pierre-Henri Tournier
In this work we describe a particle simulation method where the bulk density is periodically remapped on a coarse spline grid using a Forward-Backward Lagrangian (FBL) approac…