zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Bioeconomic modelling of a three-species fishery with switching effect. (English) Zbl 1050.92055
The authors study the problem of combined harvesting of a system involving one predator and two prey species fishery where the predator feeds more intensively on the more abundant species. They give a mathematical formulation for the optimal harvest policy and obtain its solution in the equilibrium case by using Pontryagin’s maximum principle. They also discuss dynamic optimization of the harvest policy and explain biological and bioeconomic interpretations of the results associated with the optimal equilibrium solution.

49N90Applications of optimal control and differential games
91B76Environmental economics (natural resource models, harvesting, pollution, etc.)
34D20Stability of ODE
Full Text: DOI
[1] K.J. Arrow and M. Kurz,Public Investinent, The Rate of Return and Optimal Fiscal Policy, John Hopkins, Baltimore, 1970.
[2] J.T.R. Bell,An Elementary Treatise on Co-ordinate Geometry of Three Dimensions, Macmillan, New York, 1941.
[3] K.S. Chandhuri and S. Saha Ray,Bionomic Exploitation of Lotka-Voltera Prey-Predator System, Bull. Cal. Math. Soc.83, 175--186 (1991). · Zbl 0744.34046
[4] C.W. Clark,Bioeconomic Modelling and Fisheries Management, Wiley, New York, 1985.
[5] C.W. Clark,Mathematical Bioeconomics: The Optimal management of Renewable Resources, Wiley, New York, 1990. · Zbl 0712.90018
[6] B.S. Goh, G. Leitmann and T.L. Vincent,Optimal Control of a Prey-Predator System, Math. Biosci.19 263--286 (1974). · Zbl 0297.92013 · doi:10.1016/0025-5564(74)90043-1
[7] B.S. Goh,Management and Analysis of Biological Populations, Elsevier, Amsterdam, 1980.
[8] G. Leitmann,An Introduction to Optimal Control, McGraw-Hill, New York, 1966. · Zbl 0196.46302
[9] R.M. May,Stability and Complexity in Model Ecosystems Princeton University Press, Princeton, 1974.
[10] W.W. Murdoch and A. Oaten,Predation and Population Stability, Advances in ecological Research,9, 1--131 (1975). · doi:10.1016/S0065-2504(08)60288-3
[11] L.S. Pontryagin, V.S. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko.The Mathematical Theory of Optimal processes, Wiley-Interscience, New York, 1962. · Zbl 0102.32001
[12] T. Pradhan and K.S. Chaudhuri,Bioeconomic harvesting of a schooling fish species: A dynamic reaction model, Korean J. Comput. & Appl. Math. 6(1) (1999) pp. 127--141. · Zbl 0914.92023
[13] J. Roughgarden and M. Feldman,Species Packing and Predation Pressure, Ecology,56, 489--492 (1975). · doi:10.2307/1934982
[14] W. Silvert and W. R. Smith,Optimal Exploitation of a Multi-species Community, Math. Biosci.33, 121--134 (1977). · Zbl 0371.92017 · doi:10.1016/0025-5564(77)90067-0
[15] J.H. Steele,Structure of Marine Ecosystems, Harvard University Press, Cambridge, 1974.
[16] M. Tansky,Switching Effect in prey-Predator System, J. Theor. Biol.70, 262--271 (1978). · doi:10.1016/0022-5193(78)90376-4