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Volume 5,     Number 4,     Fall 1997

 

SOLUTIONS OF TWO SPECIES
REACTION-DIFFUSION SYSTEMS
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.

 

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