In marine fisheries management, the development of suitable harvesting strategies is important for maintaining a substantial proportion of the unharvested fish population. In this paper, we study the spatial dynamics of the fish population put forward by Lundberg and Jonzen, in which the total population is distributed over two habitats, where one area is kept as a reserve and the migration of a certain proportion of adults from the reserve to the harvesting area is allowed. We find out the equilibrium populations, discuss their nature, and derive the conditions for the asymptotic stability of these equilibrium populations of this model represented by a rational system. The results obtained in this paper are useful in obtaining the optimal harvesting strategies with respect to the maximum population growth rates. We also use phase space diagrams to discuss the dynamics of the equilibrium populations.
Philip et al. (Sat,) studied this question.