STUDY ON HARVESTED POPULATION WITH DIFFUSIONAL MIGRATION

1 IntroductionBiological resources are renewable resources. Ih the eXPlOitation of population resources)both the economic benefits and the environmelltal effects must be taken icao accoullt. Theharvesting problexns on the pOPulation have been studied otensively in the literature 1--3]. Inpractical management, because of wrong exPloitation, some resouxces population are exploitedtoo heavily, and in the 6Xtreme case, are driven to 6Xtinction.In order to prevent the resources population from…

STUDY ON HARVESTED POPULATION WITH DIFFUSIONAL MIGRATION

This paper is devoted to the study of the dynamical behavior and harvesting problem of an exploited population with diffusional migration, for which a protective patch is established. We examine the effects of protective patch and harvest on the population resources and conclude that the protective patch is effective for the conservation of population resources and ecological environment, though in some cases the extinction can not be eliminated. The dangerous region, the parameters domains and the typical bifurcation curves of stability of steady states for the considered system are determined. The optimal harvest policy for the considered population is made also. The explicit expressions are obtained for the optimal harvesting effort, the maximum sustainable yield and the corre- sponding population density. Our results provide a theoretical evidence for the practical management of biological resources.