The impact on mathematics of the paper ''Oscillation and Chaos in Physiological Control Systems'' by Mackey and Glass in Science, 1977

TL;DR

This paper reviews the mathematical significance of the Mackey-Glass and similar delay differential equations in understanding oscillation and chaos in physiological control systems, highlighting developments from 1977 to 2012.

Contribution

It provides a personal overview of rigorous mathematical results related to these equations and their impact on the study of nonlinear delay differential equations in physiology.

Findings

Mathematical analysis of delay differential equations

Role of Mackey-Glass equation in chaos theory

Development of rigorous results from 1977 to 2012

Abstract

The note describes the role of the Mackey-Glass equation and of a similar equation due to Lasota in the study of nonlinear delay differential equations between 1977 and 2012, as far as rigorous mathematical results are concerned, and from the very personal point of view of the author's involvement.