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.

While my current research interests are in difference equations, I also have interests in a number of areas of interdisciplinary study. I would like to broaden my interests in the Human Genome Initiative, image processing, and/or information security. Such interests are the result of previous research and seminar experiences at Baylor College of Medicine, Sandia National Laboratories, the United States Department of Defense, and the Mathematical Sciences Research Institute.

To conclude, I am highly interested in increasing the number of persons of color who pursue Master’s and Doctoral degrees in mathematics, engineering, and the biological, social, and physical sciences. I would like to express the interest at the level of the professorate by writing grants and proposals that would fund programs designed to increase the number of persons of color who pursue advanced degrees in the areas listed above, and by contributing to the advancement of the mathematics department of which I am a member. In the future I wish to gain the tools necessary to participate in an advanced degree program in mathematics where such a program does not exist or is already in place. This may involve developing research seminars, colloquia, or graduate courses.