Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Rough Sets and Other Mathematics: Ten Research Programs Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

A Food Web Population Model in Deterministic and Stochastic Environment

verfasst von : D. Sadhukhan, B. Mondal, M. Maiti

Erschienen in: Facets of Uncertainties and Applications

Verlag: Springer India

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper deals with the selective harvesting of two species from a food chain model of three species, in which prey and predator obey the Gompertz law of growth. Initially the dynamical behaviour of the system was studied under deterministic environment. In deterministic case, the local stability of the system was also studied; we investigated the condition of global stability and the existence of the bionomic equilibrium was examined. The optimal harvesting policy is studied with the help of Pontryagin’s maximum principle. In the second part of the problem, we investigated the stability condition of the system under stochastic environment. Then a comparison is made between deterministic and stochastic cases.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel A Bi-Objective Solid Transportation Model Under Uncertain Environment
Nächstes Kapitel Computational Method for High-Order Weighted Fuzzy Time Series Forecasting Based on Multiple Partitions
Literatur
1.
Clark, C.W.: The Optimal Management of Renewable Resources. Mathematical Bioeconomic. Wiley, New York (1976)MATH
2.
Braure, F., Soudack, A.C.: Stability regions and transition phenomena for harvested predator prey systems. J. Math. Biol. 7, 319–337 (1979)MathSciNetCrossRef
3.
Braure, F., Soudack, A.C.: Stability regions in predator prey systems with constant—rate prey harvesting. J. Math. Biol. 8, 55–71 (1979)MathSciNetCrossRef
4.
Myerscough, M.R., Gray, B.F., Hogarth, W.L., Norbury, J.: An analysis of an ordinary differential equation model for a two species predator-prey system with harvesting and stocking. J. Math. Biol. 30, 389–411 (1992)MathSciNetCrossRef
5.
Dia, G., Tang, M.: Coexistence region and global dynamics of a harvested predator prey systems. SIAM J. Appl. Math. 58, 193–210 (1998)MathSciNetCrossRef
6.
Xiao, D., Ruan, S.: Bogdanov-Takens bifurcations in predator-prey systems with constant rate harvesting. Fields Inst. Commun. 21, 493–506 (1999)MathSciNetMATH
7.
Chaudhuri, K.S.: A bioeconomic model of harvesting a multispecies fishery. Ecol. Model. 32, 267–279 (1986)CrossRef
8.
Chaudhuri, K.S.: Dynamic optimization of combined harvesting of a two species fishery. Ecol. Model. 41, 21–25 (1987)
9.
Kar, T.K., Chaudhuri, K.S.: On non selective harvesting of a multispecies fishery. Int. J. Math. Educ. Sci. Technol. 33(4), 543–556 (2002)MathSciNetCrossRef
10.
Kar, T.K., Chaudhuri, K.S.: Regulation of a prey-predator fishery by taxation. Int. J. Math. Educ. Sci. Technol. 34(3), 543–556 (2003)MathSciNetMATH
11.
Purohit, D., Chaudhuri, K.S.: A bioeconomic model of non selective harvesting of two competing fish species. Int. J. Math. Educ. Sci. Technol. 33(4), 543–556 (2002)CrossRef
12.
Chaudhuri, K.S., SahaRay, S.: On the combined harvesting of a prey-predator system. J. Biol. Syst. 4, 376–389 (1996)CrossRef
13.
Dubey, B., Chandra, P., Sinha, P.: A model of fishery resource with reserve area. Nonlinear Anal. Real World Appl. 4, 625–637 (2003)MathSciNetCrossRef
14.
Kar, T.K., Mishra, S.: Influence of prey reserve in a prey-predator fishery. Nonlinear Anal. 65, 1725–1735 (2006)MathSciNetCrossRef
15.
Kar, T.K., Matsuda, H.: Controllability of a harvested prey-predator system with time delay. J. Biol. Syst. 14(2), 243–254 (2006)CrossRef
16.
Kar, T.K., Pahari, U.K.: Modelling and analysis of a prey-predator system with age-structure and harvesting. Nonlinear Anal. 8, 601–609 (2007)CrossRef
17.
Kar, T.K.: Selective harvesting in a prey-predator fishery with time delay. Math. Comput. Model. 38, 449–458 (2003)MathSciNetCrossRef
18.
Kar, T.K., Chaudhuri, K.S.: On selective harvesting of two competing fish species in the presence of environmental fluctuation. Nat. Resour. Model. 17(3), 251–273 (2004)MathSciNetCrossRef
19.
Beddington, J.R., May, R.M.: Harvesting populations in a randomly fluctuation environment. Science 197, 463–465 (1977)CrossRef
20.
May, R.M., Beddington, J.R., Horwood, J.W., Shepherd, J.G.: Exploiting natural populations in an uncertain world. Math. Biosci. 42, 219–252 (1978)MathSciNetCrossRef
21.
Ludwig, D.A.: Harvesting strategies for randomly fluctuating populations. J. du Conseil International pour l’Exploration de la Mer 39, 166–174 (1980)
22.
23.
Hanson, F.B.: Analysis of a singular fluctuation delay equation that arises from the stochastic modelling of population growth. J. Math. Appl. 96, 405–419 (1982)
24.
25.
Turelli, M.: A reexamination of stability in random varying environments with comments on stochastic theory of limiting similarity. Theor. Popul. Biol. 13, 244–267 (1978)MathSciNetCrossRef
26.
Kar, T.K., Chaudhuri, K.S.: Harvesting in a two prey one predator fishery: a bioeconomic model. Aust. N. Z. Ind. Appl. Math. J. 45, 443–456 (2004)MathSciNetMATH
27.
Sadhukhan, D., Sahoo, L.N., Mondal, B., Maiti, M.: Food chain model with optimal harvesting in fuzzy environment. J. Appl. Math. Comput. 1(2), 1–2 (2009)MathSciNetMATH
28.
Sutinen, J.G., Andersen, P.: The economics of fisheries law enforcement. Land Econ. 61, 387–397 (1985)CrossRef
29.
Pradhan, T., Chaudhuri, K.S.: Bioeconomic modelling of a single species fishery with Gompertz law of growth. J. Biol. Syst. 6(4), 393–409 (1998)CrossRef
30.
Gikhman, I.I., Skorokhod, A.V.: The Theory of Stochastic Processes, vol. I. Springer, Berlin (1974)
31.
Gikhman, I.I., Skorokhod, A.V.: The Theory of Stochastic Processes, vol. II. Springer, Berlin (1975)
32.
Gikhman, I.I., Skorokhod, A.V.: The Theory of Stochastic Processes, vol. III. Springer, Berlin (1979)
33.
Afanas’ev, V.N., Kolmanowski, V.B., Nosov, V.R.: Mathematical Theory of Global Systems Design. Kluwer Academic, Dordrecht (1996)CrossRef
Metadaten
Titel
A Food Web Population Model in Deterministic and Stochastic Environment
verfasst von
D. Sadhukhan
B. Mondal
M. Maiti
Copyright-Jahr
2015
Verlag
Springer India
Buch
Facets of Uncertainties and Applications

Print ISBN: 978-81-322-2300-9

Electronic ISBN: 978-81-322-2301-6

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-81-322-2301-6_21