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Toxicity in plants and optimal growth under fertilizer

  • D. K. Bhattacharya
Article

Abstract

The paper determines by control-theoretic means the optimal dose of fertilizer to be used to two plants for maintaining optimal revival of their growths, which are retarded mainly due to the toxicity contributed by the plants jointly.

AMS Mathematics Subject Classification

34C 34D 34H 92 93 

Key words and phrases

Toxicity in plants bionomic equilibrium Pontryagin's maximum principle 

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References

  1. 1.
    B. S. Goh,Management and analysis of biological populations, Elsvier Science Publishing Company, Amsterdam, Oxford, New York, 1980.Google Scholar
  2. 2.
    C. W. Clark,Bionomic modeling and fisheries management, Wiley Eastern, New York, 1985.Google Scholar
  3. 3.
    C. W. Clark,Mathematical Bioeconomics. The optimal management of renewable resources, Wiley Eastern, New York, 1976, 1990.MATHGoogle Scholar
  4. 4.
    D. K. Bhattacharya and S. Begum,A note on bionomic equilibrium of two species system—I, Mathematical Biosciences135 (1996), 111–127.MATHCrossRefGoogle Scholar
  5. 5.
    D. K. Bhattacharya and S. Begum,Bionomic equilibrium and optimization of revnue, Jour. Pure. Math. (India)15 (1998), 105–120.MATHMathSciNetGoogle Scholar
  6. 6.
    D. K. Bhattacharya and S. Karan,Pest Management of Two non-interacting pests in presence of common predator, J. Appl. Math. & Computing (accepted), 2003.Google Scholar
  7. 7.
    H. I. Freedman and J. B. Sukla,Models for the effect of toxicant in single species and predator- prey systems, Jour. Mathematical Biology,30 (1990), 15–30.CrossRefGoogle Scholar
  8. 8.
    J. Chattopadhyay, G. Ghosal and K. S. Chaudhury,Non selective harvesting of a prey predator community with infected prey, Korean J. Comput. & Appl. Math.6 (1999), 601–616.MATHMathSciNetGoogle Scholar
  9. 9.
    J. Chatterjee,Effect of toxic substances on a two-species competive system, Ecol. Modeling84 (1996), 287–289.CrossRefGoogle Scholar
  10. 10.
    J. Maynard-Smith,Models in Ecology, Cambridge University Press, 1974.Google Scholar
  11. 11.
    K. S. Chaudhury,Dynamic optimization of combined harvesting of a two species fishery, Ecol. Modeling41 (1986), 17–25.CrossRefGoogle Scholar
  12. 12.
    T. J. De Luna and T. G. Hallam,Effects of toxicants on populations; a-qualitative approach IV. Resource—consumer toxicant models, Ecol. Model35 (1987), 249–273.CrossRefGoogle Scholar
  13. 13.
    T. G. Hallam and C. E. Clark,Non-autonomus logistic equations as models of populations in a deteriorating environment, Jour. Theo. Biol.93 (1982), 303–311.CrossRefMathSciNetGoogle Scholar
  14. 14.
    T. G. Hallam and T. J. De Luna,Effects of toxicants on populations, a-qualitative approach III. Environmental and food chain pathways, Jour. Theo. Biol.109 (1984), 411–429.CrossRefGoogle Scholar
  15. 15.
    T. G. Hallam, C. E. Clark and G. S. Jordan,Effects of toxicants on populations, Jour. Math. Biol.18 (1983a), 25–37.MATHGoogle Scholar
  16. 16.
    T. G. Hallam, C. E. Clark and R. R. Lassiter,Effects of toxicants on populations, aqualitative approach I. Equilibrium environmental exposure, Ecol. Model.18 (1983b), 291–304.CrossRefGoogle Scholar
  17. 17.
    T. Pradhan and K. S. Chudhury,Bioeconomic harvesting of a schooling fish species: A dynamic reaction model, Korean J. Comput. & Appl. Math.,6 (1999), 127–142.MATHMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2004

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of CalcuttaKolkataIndia

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