Monotone dynamical systems: Reflections on new advances & applications

Abstract

The article contains the author's reections on recent developments in a very select portion of the now vast subject of monotone dynamical systems. Continuous time systems generated by cooperative systems of ordinary differential equations, delay differential equations, parabolic partial differential equations, and control systems are the main focus and results are included which the author feels have had a major impact in the applications. These include the theory of competition between two species or two teams and the theory of monotone control systems.