  The present paper deals with a prey-predator model with prey refuge
proportion to both species and independent harvesting of each species. Our
study shows that using refuge as control, it can break the limit circle of the
system and reach the required state of equilibrium level. It is established the
optimal harvesting policy. The boundedness, feasibility of interior equilibria,
bionomic equilibrium have been determined. The main observation is that
coefficient of refuge plays an important role in regulating the dynamics of the
present system. Moreover the variation of the coefficient of refuge change the
system from stable to unstable and vice-versa. Some numerical illustration are
given in order to support of our analytical and theoretical findings.
