Spatial Competition Model:
Nonlinear Reaction-Diffusion PDEs
I am looking at a 3-species spatial competition model. The equations
are similar to those of the well known Lotka-Volterra predator-prey
system, with appropriate variations, including:
- three equations instead of two
- inclusion of diffusion terms in one of the equations
- variation in the nonlinear "reaction" portion of each equation
(resembling those of the Fisher equation)
Current work focuses on qualitative analysis of the solutions
(especially examining the existence of traveling waves), and
eventually obtaining some numerical results. The system was designed
to model the population dynamics and interactions of three plant
species in the riparian (river) environment of New Mexico. The native
cottonwood trees are declining in numbers, while two exotic or
non-native species, namely Russian olives and tamarisks (salt cedars),
have been spreading. It should be noted that the mathematical model
is general enough that it could be applied to other sets of species.