Oscillations in Dynamic Models of the Wilson-Cowan Type System

Abstract

A review of samples of oscillations in a system of ordinary differential equations that arise in mathematical models of complex networks is provided. Starting from the low-dimensional systems, we go up in the sense of system dimensionality, commenting on various patterns that appear. We overlook examples of relatively large systems (with dimensionality up to 13 equations) that describe leukemia treatment and cellular aging. Visualizations and examples are supplied. The methods used are of geometrical and computational nature, revealing phase space structures and specifics.