3 papers
math.AP2026
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…
q-bio.TO2026
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…
math.AP2026
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…