Universit ́e Fran ̧cois Rabelais 2019
Institut Denis Poisson
Master Thesis Proposal : Yves Belaud
Title : Monotone Dynamical Systems
In the field of ecology, competition is an important topic. It can occur between individuals of the same
species, called intraspecific competition, or between different species, called interspecific competition. In
this case, when resources are limited, several species may depend on these resources. Thus, each of the
species competes with the others to gain access to the resource. These models of competition are converted
into a system of equations. The solution of the equations describes how the biological system behaves.
The main purpose of this Master Thesis is a study of the mathematical tools for a large class of systems
involved in this field.
References :
(1) Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Co-operative Systems, Mathematical Surveys and Monographs, Volume 41, Hal L. Smith, American Math-
ematical Society (1995).
(2) Mathematical Biology I., J.D. Murray, Springer (2002).
(3) Mathematical Biology II., J.D. Murray, Springer (2003).
