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Pest management of two non-interacting pests in presence of common predator. (English) Zbl 1047.34033
The authors study a mathematical model, consisting of 3 ODEs of first order. They derive conditions for the existence of a globally asymptotically stable equilibrium. Possibilities for controling such system are also discussed.

MSC:
34C11 Growth and boundedness of solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
34H05 Control problems involving ordinary differential equations
92D40 Ecology
93C15 Control/observation systems governed by ordinary differential equations
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[1] B.S. Goh, J. Leitman, and T.L. Vincent,Optimal control of a Prey-Predator system, Math. B.R., Mathematical Biosciences 19, 1974, pp. 263–286. · Zbl 0297.92013 · doi:10.1016/0025-5564(74)90043-1
[2] B.S. Goh, 1980;Management and analysis of biological Population, Elsvier Scientific pub. company, Amsterdam, Oxford, New York, 1980.
[3] C. B. Huffaker,New technology of pest control, Wiley-Interscience, New York, 1980.
[4] C.W. Clark,The optimal management of renewable resources, Math Bioeconomics, Wiley Eastern, New York, 1976, 1990. · Zbl 0364.90002
[5] D.C. Hall and B.R. Norgaard,On the time and application of pesticides, Amer. J. Agriculture Eco, 55, pp. 198–201, 1973. · doi:10.2307/1238437
[6] D. K. Bhattacharya and S. Begum,A note on bionomic equilibrium of two species system-1; Math. Biosciences, 135, 1996 pp.-111–127. · Zbl 0856.92018
[7] D. K. Bhattacharya and S. Karan,On bionomic model of integrated pest management of a single pest population, (accepted) the journal of Differential equation and Dynamical Systems, 2003.
[8] D.K. Bhattacharya and S. Karan (2002)Pest management of a single density dependent pesi- communicated to REVISTA DE LA ACADEMIA, SPAIN, 2002.
[9] J. Chattopadhyay, G. Goshal and K.S. Chaudhury,Nonselective harvesting of a prey predator community with infected prey, Korean J. of Comput. and Appl. Math., Vol. 6 (1999), pp. 601–616. · Zbl 0938.92031
[10] R.L. Matcalf and W.H. LuckmannIntroduction to insect pest management Wiley-Interscience, New York, 1975.
[11] T. Pradhan and K.S. ChoudhuryBioeconomic harvesting of a schooling fish species: A dynamic reaction model, Korean J. of Comput. and Appl. Math., Vol. 6(1999), pp. 127–142. · Zbl 0914.92023
[12] T.L. Vincent,pest Management problems via optimal control theory, Biometrics 31, 1975, pp. 1–10. · Zbl 0307.92016 · doi:10.2307/2529704
[13] V.M. Stern and R.F. Smith, R. VAN Den Boszh and K.S. Hogan,The Integrated control concept. Hilgardia, 29, 1959, pp. 81–101.
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