BIOECONOMIC MODELLING OF A THREE-SPECIES FISHERY WITH SWITCHING EFFECT

  • Samanta, G.P. (Department of Mathematics, Bengal Engineering College) ;
  • Manna, Debasis (Department of Mathematics, Bengal Engineering College) ;
  • Maiti, Alakes (Department of Mathematics, Taki Government College)
  • 발행 : 2003.05.01

초록

This paper aims to study the problem of combined harvesting of a system involving one predator and two prey species fishery in which the predator feeds more intensively on the more abundant species. Mathematical formulation of the optimal harvest policy is given and its solution is derived in the equiblibrium case by using Pontryagin's Maximum principle. Dynamic optimization of the harvest policy is also discussed by taking E(t), the combined harvest effort, as a dynamic variable. Biological and bioeconomic interpretations of the results associated with the optimal equilibirum solution are explained. The significance of the constraints required for the existence of an optimal singular control are also given.

키워드

참고문헌

  1. Public Investment, The Rate of Return and Optimal Fiscal Policy K.J. Arrow;M. kurz
  2. An Elem entary Treatise on Co-ordinate Geometry of Three Dimensions J.T.R. Bell
  3. Bull. Cal. Math. Soc. v.83 Bionomic Exploitation of Lotka-Voltera Prey-Predator System K.S. Chaudhuri;S. Saha Ray
  4. Bioeconomic Modelling and Fisheries Management C.W. Clark
  5. The Optimal management of Renewable Resources C.W. Clark
  6. Math. Biosci v.19 Optimal Control of a Prey-Predator System B.S. Goh;G. Leitmann;T.L. Vincent
  7. Management and Analysis of Biological Populations B.S. Goh
  8. An Introduction to Optimal Control G. Leitmann
  9. Stability and Complexity in Model Ecosystems R.M. May
  10. Advances in ecological Research v.9 Predation and Population Stability W.W. Murdoch;A. Oaten
  11. The Mathematical Theory of Optimal processes L.S. Pontryagin;V.S. Boltyanskii;R.V. Gamkrelidze;E.F. Mishchenko
  12. Korean J. Comput. & Appl. Math. v.6 no.1 Bioeconomic harvesting of a schooling fish species : A dynamic reaction model T. Pradhan;K.S. Chaudhuri
  13. Ecology v.56 Species Packing and Prdation Pressure J. Roughgarden;M. Feldman
  14. Math. Biosci. v.33 Optimal Exploitation of a Multi-species Community W, Silvert;W.R. Smith
  15. Structure of Marine Ecosystems J.H. Steele
  16. J. Theor. Biol v.70 Switching Effect in prey-Predator System M. Tansky