Volume 5, Number 4, Fall 1997
SOLUTIONS OF TWO SPECIES
ALAN EASTON, MANMOHAN SINGH AND GURONG CUI
Abstract. Reaction-diffusion equations describe interactions
in a variety of systems in disciplines such as biology.
An understanding of the behavior of the systems is often
drawn from qualitative analyses since analytical solutions are
difficult to obtain. Numerical approaches provide a key to
discovering the behavior of the time dependent solutions.
We consider three two species ecological systems: a predator-prey
system, a competing species system and a mutualism
system. They have been solved using an operator splitting
method which can be readily extended for solving multi-species
non linear reaction diffusion equations.
The evolution of the biological systems and the steady
state solutions in the form of travelling waves are accurately
presented for each model. These solutions include phenomena
such as waves of pursuit and evasion, competitive exclusion
and cooperation for mutual advantage.