Journal of Biological Systems, Vol. 11, No. 1 (2003) 27–41 c  World Scientiﬁc Publishing Company A MODEL FOR AN INSHORE-OFFSHORE FISHERY B. DUBEY Mathematics Group, Birla Institute of Technology and Science, Pilani – 333 031, India bdubey@bits-pilani.ac.in P. SINHA * and P. CHANDRA † Department of Mathematics, Indian Institute of Technology, Kanpur – 208 016, India * prawal@iitk.ac.in † peeyush@iitk.ac.in Received 12 January 2002 Revised 8 August 2002 In this paper, a nonlinear mathematical model to study the dynamics of an inshore- oﬀshore ﬁshery under variable harvesting is proposed and analyzed. Criteria for local stability, instability and global stability of the system are derived. The optimal harvest- ing policy is discussed by considering taxation as a control instrument. It is shown that the ﬁshery resources can be protected from overexploitation by increasing the tax and discount rates. Keywords : Fishery resource; optimal harvesting; taxation. 1. Introduction The optimal management of renewable resources such as ﬁshery and forestry is very important as they are directly linked to sustainable development. With the devel- opment of modern technology, these resources are overexploited to make maximum proﬁt. Economic and biological management of renewable resources have been dis- cussed by many researchers [1, 5–10, 16, 19–22]. Clark and De Pree [9] investigated the implication of restricted malleability of capital for the optimal exploitation of a renewable resource stock. Kitabatake [18] presented a dynamic model for ﬁshery resources and showed that the use of diesel-powered trawling may lead to the extinc- tion of predator as well as prey species if the trawling eﬃciency in the catch of prey species is improved. Chaudhuri [11] studied the problem of combined harvesting of two competing ﬁsh species and showed that open-access ﬁshery may have a bionomic equilibrium implying the extinction of one of the species. Mesterton-Gibbons [20] proposed a model to study the optimal policy for the combined harvesting of two ecologically independent species and obtained criteria for the survival of less pro- ductive species as a function of the system parameters and initial stocks. This work was further extended to study an optimal policy for maximizing the present value 27