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.
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.