Shurron Farmer

Born: October 26, 2972 in Tallahassee, FL; raised in Quincy, FL

BS mathematics (1994) Florida A&M University; M.S. Mathematics (1996) Howard University

Ph.D. mathematics(2001) Howard University
thesis: ; Advisor: Prof. A.A. Yakubu

Assistant professor of mathematics, Morgan State University

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STATEMENT: My current research interests are primarily in the areas of difference equations and mathematical biology. Under the supervision of Professor Abdul-Aziz Yakubu, I have used the theory of discrete dynamical systems to analyze a two-age class (juvenile and adult) single species, discrete-time climax population model.

Climax species are species that may go extinct at small population densities but have a set of initial population densities that do not lead to extinction. The oak trees Quercus leucotrichophora and Quercus floribunda are examples of climax species. In a single species climax population model with no age structure, high population densities lead to extinction. Studies of discrete-time models of climax species with age structure are rare in the literature. In my research, I have shown that age structure makes it possible for a density that has extinction as its ultimate life history to have persistence as its ultimate fate with juvenile-adult competition. This suggests that juvenile-adult competition may be critical to species survival. Finally, I have applied the results of my research to several population models that are or are not capable of generating chaotic dynamics such as supporting chaotic attractors. I have also applied the results of my research to population data of the purse-seine anchovy fish, Engraulis capensis, which is located off the West Cape coast of South Africa.

In my research, I have analyzed a climax population model in which only juveniles reproduce and all juveniles become adults. In the future, I would like to continue my research of climax population models by:
1. Establishing a global stability result about the model I currently study;
2. Studying models where juveniles and adults both reproduce and models where not all juveniles become adults;
3. Research the effects of dispersion on juvenile-adult competition.


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