Professor Emeritus

Department of Mathematics

Interdisciplinary Program in Applied Mathematics

University of Arizona

Tucson, AZ 85721 USA

My research
involves the derivation and analysis of mathematical models that
describe population and evolutionary dynamics. I use methods from
dynamical systems theory (such as stability analysis and bifurcation
theory) applied to a variety of equations types, including difference
equations, matrix equations, ordinary and partial differential
equations, integro-difference equations, and functional delay
equations. I am particularly interested in structured population
dynamics, which is a modeling methodology that accounts for different
classifications of individuals within a population or species (age
classes, size classes, life cycle stages, etc.). A basic goal is to
understand how the characteristics of these classes -- their survival
rates, birth rates, competitive interactions, evolutionary adaptation,
etc. -- affect a population's dynamics, especially with regard to
extinction versus survival and the long term nature of the dynamics
(equilibration, periodic oscillation, chaos, etc.). I am also study
evolutionary game theoretic versions of population models.

Currently I
collaborate with Shandelle
Henson and Jim
Hayward on the dynamics of seabird populations (see the Seabird EcologyTeam
webpage and also the article Nature
makes sense).
In the past I have had interdisciplinary collaborations with the
late Tom Vincent and with Robert
Costantino on applications of evolutionary game theory in ecology,
and with the Robert Costantino, Robert Desharnais, Brian Dennis, Shandelle Henson and Aaron King (the Beetle
Team) on experimental nonlinear dynamics. Some readings about some
of these research studies are found in my list
of publications and in the following books and articles :

Chaos in Ecology: Experimental Nonlinear Dynamics by J. M. Cushing, R. F. Costantino, B. Dennis, R. A. Desharnais, S. M. Henson, Academic Press, 2003

*Matrix
Population Models: Construction, Analysis, and Interpretation *(Second
Edition) by Hal Caswell, Sinauer Associates Inc., 2001

Self-Organization
in Complex Ecosystems by Recard V. Solé and Jordi
Bascompte, Princeton University Press, Princeton, New Jersey, 2006

*Stability in Model
Populations* by Laurence D. Mueller and Amitabh Joshi,
Monographs in Population Biology 31, Princeton University Press,
Princeton, New Jersey, 2000

Mathematicians
show
how beetles can share a niche by Patrick Barry, Science News, Vol. 175 #3
(2009), January 31, p 14.

*What's Happening
in the Mathematical Sciences 1998-1999* by Barry Cipra, published by
the American Mathematical Society (ISBN 0-8218--0766-8)

*Boom time for beetles* by Jonathan Knight, New Scientist, 29 November 1997

*Chaotic Bugs
Make the Leap from Theory to Experiment* by Barry Cipra, *SIAM
NEWS*, July/August 1997

*Chaotic beetles*
by H. C. Godfray and M. P. Hassell, Science
275 (1997)

*Chaos in a cup
of flour* by P. Rohani and D.J.D. Earn, *Trends in Ecology and
Evolution* 12 (1997)

J. M. Cushing / Department of Mathematics
/ Program in Applied
Mathematics / University
of Arizona / Tucson, AZ 85721-0089

(revised 9 February 2022)

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