  The Lotka-Volterra model of competition has been studied by numerical
simulations using the Runge-Kutta-Fehlberg algorithm. The stable fixed points,
unstable fixed point, saddle node, basins of attraction, and the separatices
are found. The transient behaviours associated with reaching the stable fixed
point are studied systematically. It is observed that the time of reaching the
stable fixed point in any one of the basins of attraction, depends strongly on
the initial distance from the separatrix. As the initial point approached the
separatrix, this time was found to diverge logarithmically. The divergence of
the time, required to reach the stable fixed point, indicates the critical
slowing down near the critical point in equilibrium phase transition. A
metastable behaviour was also observed near the saddle fixed point before
reaching the stable fixed point.
