4 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…