Shurron Farmer

Personal

First Name: Shurron
Last Name: Farmer

Education

Degree: Ph.D.
Graduation Year: 2001

Degree: M.S.
Graduation Year: 1996
Major: Mathematics

Degree: B.S.
Graduation Year: 1994
Major: Mathematics

Summary

Assistant Professor of Mathematics at Morgan State University interested in difference equations and mathematical biology.

Biography

Shuron Farmer was born in Tallahassee, FL and raised in Quincy, FL.  He attended Florida A&M University as an undergraduate student and then finished both his masters and Ph.D. at Howard University in mathematics.  His advisor was Professor Abdul-Aziz Yakubu.  Dr. Farmer currently is an Assistant Professor of Mathematics at Morgan State University.  His research interests are below.

Research

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.

 

Lifetime

Year Born: 1972