Presenter: Braden Carlson
Authors: Braden Carlson
Faculty Advisor: Jianlong Han
Institution: Southern Utah University
In recent decades, scientists have observed that mortality rate of some competing species increases superlinearly as populations grow to unsustainable levels. This is modeled by terms representing crowding effects in the following system of nonlinear differential equations that describes population growth of two species competing for resources under the effects of crowding. After applying nondimensionalization to reduce parameters in the system, the stability of the four steady-state solutions is examined. A semi-implicit numerical scheme is proposed and studied that guarantees positivity of the approximate solutions to the system.