Date of Award


Degree Type


Degree Name

Doctor of Philosophy in Mathematics



First Advisor

Mustafa Kulenović


This dissertation focuses on difference equations that are of a certain type, non-autonomous competitive and cooperative systems. Previously, systems of this nature were investigated for the single species model. Here, this investigation extends to the case of two species or more, corresponding to a two dimensional system all the way to an n dimensional system. The purpose is to establish global attractivity results for these systems through a method using difference inequalities along with Northeast and Southeast partial ordering for competitive and cooperative systems, respectively. The non-autonomous case of some systems, established and well-known, are discussed for purpose of comparing the process in which global results are achieved. Finally, these systems will be applied to evolutionary dynamics by creating an evolutionary model of the system using an original process.



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