Biomedical subjects

Michael Bestehorn

Publications and source records attributed to Michael Bestehorn.

4 recordsLinked to original sources

PubMed2003

Activity dynamics in nonlocal interacting neural fields.

We study the activity of a synaptically coupled neuronal network consisting of an excitatory and an inhibitory layer with isotropic connections and nonlinear interactions. Using the mathematical model of Wilson and Cowan in two spatial dimensions, we first discuss a spatial hysteresis phenomenon. Then we analyze special traveling wave solutions with stationary shape. We establish existence conditions, derive analytic expressions of the particular solutions and their velocity, and finally present numerical simulations.

Animals↗

PubMed2003

Pattern formation in intracortical neuronal fields.

This paper introduces a neuronal field model for both excitatory and inhibitory connections. A single integro-differential equation with delay is derived and studied at a critical point by stability analysis, which yields conditions for static periodic patterns and wave instabilities. It turns out that waves only occur below a certain threshold of the activity propagation velocity. An additional brief study exhibits increasing phase velocities of waves with decreasing slope subject to increasing activity propagation velocities, which are in accordance with experimental results. Numerical studies near and far from instability onset supplement the work.

Action Potentials↗

PubMed1994

Motion of defects in rotating fluids.

We study defect motion in a rotating convection cell. We present numerical results of a generalized Swift-Hohenberg equation, which provides a model description of the vertically averaged three-dimensional (3-D) hydrodynamic equations. Our model includes non-Boussinesq effects. It also accounts for the effects of the Coriolis force induced by a rotation of the fluid layer around its vertical symmetry axis. We show that even a slow rotation well below the Kuppers-Lortz instability causes defect motion perpendicular to the convective rolls. We derive an analytic estimation of that motion.

Journal Article↗

PubMed1994

Stability of fronts separating domains with different symmetries in hydrodynamical instabilities.

A generalization of the Swift-Hohenberg (SH) equation is used to study several stationary patterns that appear in hydrodynamical instabilities. The corresponding amplitude equations allow one to find the stability of planforms with different symmetries. These results are compared with numerical simulations of a generalized SH equation (GSHE). The transition between different symmetries, the hysteretic effects, and the characteristics of the defects observed in experiments are well reproduced in these simulations. The existence of steady fronts between domains with different symmetries is also analyzed. Steady domain boundaries between hexagons and rolls, and between hexagons and squares are possible solutions in the amplitude equation framework and are obtained in numerical simulations for a full range of coefficients in the GSHE.

Journal Article↗