Necessary optimality conditions for predator-prey system with a hunter population

• Autorzy: Apreutesei N. C.
• Języki publikacji: EN

Abstrakty

EN

An optimal control problem is studied for a predator-prey reaction-diffusion system. A hunter population is introduced in the ecosystem and it is interpreted as a control variable. One finds necessary optimality conditions in order that, in the end of a given time interval, the total density of the two populations is maximal.

Słowa kluczowe

EN

predator-prey system; optimal control; adjoint system

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2010
• Tom: Vol. 30, no. 4
• Strony: 389--397
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Apreutesei N. C.

• Technical University "Gh. Asachi" Iasi Department of Mathematics 11, Bd. Carol I, 700506 Iasi, Romania,

Bibliografia

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• [2] N. Apreutesei, An optimal control problem for prey-predator system with a general functional response, Appl. Math. Let. 22 (2009) 7, 1062–1065.
• [3] N. Apreutesei, G. Dimitriu, Optimal control for Lotka-Volterra systems with a hunter population, Springer, Lecture Notes in Computer Science 4818 (2008), 277–284.
• [4] V. Barbu, Mathematical Methods in Optimization of Differential Systems, Kluwer Academic Publishers, Dordrecht, 1994.
• [5] P. Georgescu, Y.H. Hsieh, Global dynamics for a predator-prey model with stage structure for predator, SIAM J. Appl. Math. 67 (2007), 1379–1395.
• [6] P. Georgescu, H. Zhang, An impulsively controlled predator-pest model with disease in the pest, Nonlinear Anal. Real World Appl. 11 (2010), 270–287.
• [7] I. Hrinca, An optimal control problem for the Lotka-Volterra system with diffusion, Panamer. Math. J. 12 (2002) 3, 23–46.
• [8] J.D. Murray, Mathematical Biology, Springer Verlag, Berlin-Heidelberg-New York, 3rd ed., 2002.