January  2017, 37(1): 485-504. doi: 10.3934/dcds.2017020

Monotone dynamical systems: Reflections on new advances & applications

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA

Received  April 2016 Revised  July 2016 Published  November 2016

Fund Project: The author is supported by a Simons Foundation Grant 355819

The article contains the author's reflections on recent developments in a very select portion of the now vast subject of monotone dynamical systems. Continuous timesystems generated by cooperative systems of ordinary differential equations, delay differential equations, parabolic partial differential equations, and controlsystems 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 betweentwo species or two teams and the theory of monotone control systems.

Citation: Hal L. Smith. Monotone dynamical systems: Reflections on new advances & applications. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 485-504. doi: 10.3934/dcds.2017020
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show all references

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