A model for fishery resource with reserve area

Nonlinear Analysis: Real World Applications

Volumn 4, Issue 4, 2003, Pages 625-637

  Dubey, B ^a   Chandra, Peeyush ^b   Sinha, Prawal ^b  

^a BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE   (India)

^b INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Fishery resource; Harvesting; Reserved zone; Stability

Indexed keywords

EID: 0037412206     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1468-1218(02)00082-2     Document Type: Article

References (32)

1. D.K. Bhattacharya, S. Begum, Bionomic equilibrium of two species system, Math. Biosci. 135 (2) (1996) 111-127.
2. G. Birkhoff, G.S. Rota, Ordinary Differential Equations, Ginn, Boston, 1882.
3. D.N. Burges, A. Graham, Introduction to Control Theory Including Optimal Control, Wiley, New York, 1980.
4. J. Chattopadhyay, A. Mukhopadhyay, P.K. Tapaswi, A resourced based competitive system in three species fishery, Nonlinear Stud. 3 (1996) 73-83.
5. C.W. Clark, Profit maximization and the extinction of animal species, Journal of Political Economy 81 (1973) 950-961.
6. C.W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources, Wiley, New York, 1976.
7. C.W. Clark, Mathematical models in the economics of renewable resources, SIAM Rev. 21 (1979) 81-99.
8. C.W. Clark, Bioeconomic Modelling and Fisheries Management, Wiley Interscience, New York, 1985.
9. C.W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources, Wiley, New York, 1990.
10. C.W. Clark, F.H. Clarke, G.R. Mundro, The optimal exploitation of renewable resource stocks: problems of irreversible investment, Econometrica 47 (1) (1979) 25-47.
11. C.W. Clark, J.D. De Pree, A simple linear model for the optimal exploitation of renewable resources, Appl. Math. Optim. 5 (1979) 181-196.
12. K.S. Chaudhuri, A bioeconomic model of harvesting a multispecies fishery, Ecol. Model. 32 (1986) 267-279.
13. K.S. Chaudhuri, Dynamic optimisation of combined harvesting of a two species fishery, Ecol. Model. 41 (1988) 17-25.
14. B. Dubey, P. Chandra, P. Sinha, A resource dependent fishery model with optimal harvesting policy, J. Biol. Systems 10 (2002) 1-13.
15. M. Fan, K. Wang, Optimal harvesting policy for single population with periodic coefficients, Math. Biosci. 152 (1998) 165-177.
16. S. Ganguli, K.S. Chaudhuri, Regulation of a single-species fishery by taxation, Ecol. Model. 82 (1995) 51-60.
17. B.S. Goh, Management and Analysis of Biological Populations, Elsevier, Amsterdam, 1980.
18. F.B. Hanson, D. Ryan, Optimal harvesting with both population and price dynamics, Math. Biosci. 148 (1998) 129-146.
19. Y. Kitabatake, A dynamic predator-prey model for fishery resources: a case of Lake Kasumigaura, Environ. Planning A 14 (1982) 225-235.
20. J. La Salle, S. Lefschetz, Stability by Liapunov's Direct Method with Applications, Academic Press, New York, London, 1961.
21. A. Leung, A. Wang, Analysis of models for commercial fishing: mathematical and economical aspects, Econometrica 44 (2) (1976) 295-303.
22. M. Mesterton-Gibbons, On the optimal policy for combined harvesting of independent species, Nat. Res. Model. 2 (1987) 109-134.
23. M. Mesterton-Gibbons, On the optimal policy for combined harvesting of predator-prey, Nat. Res. Model. 3 (1988) 63-90.
24. M. Mesterton-Gibbons, A technique for finding optimal two species harvesting policies, Ecol. Model. 92 (1996) 235-244.
25. A. Mukhopadhyay, J. Chattopadhyay, P.K. Tapaswi, Selective harvesting in a two species fishery model, Ecol. Model. 94 (1997) 243-253.
26. T. Pradhan, K.S. Chaudhuri, Bioeconomic modelling of a single-species fishery with Gompertz law of growth, J. Biol. Systems 6 (4) (1998) 393-409.
27. T. Pradhan, K.S. Chaudhuri, A dynamic reaction model of a two species fishery with taxation as a control instrument: a capital theoretic analysis, Ecol. Model. 121 (1999) 1-16.
28. T. Pradhan, K.S. Chaudhuri, Bioeconomic harvesting of a schooling fish species: a dynamic reaction model, Korean J. Comput. Appl. Math. 6 (1) (1999) 127-141.
29. T. Pradhan, K.S. Chaudhuri, Bioeconomic modelling of selective harvesting in an inshore-offshore fishery, Differential Equations Dyn. Systems 7 (3) (1999) 305-320.
30. D.L. Ragozin Jr., G. Brown, Harvest policies and nonmarket valuation in a predator-prey system, J. Environ. Econom. Manage. 12 (1985) 155-168.
31. X. Song, L. Chen, Optimal harvesting and stability for a two-species competitive system with stage structure, Math. Biosci. 170 (2) (2001) 173-186.
32. X. Zhang, L. Chen, A.U. Neumann, The stage structured predator-prey model and optimal harvesting policy, Math. Biosci. 168 (2) (2000) 201-210.