An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System

N. C. Apreutesei

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 6, page 180-195
  • ISSN: 0973-5348

Abstract

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An optimal control problem is studied for a predator-prey system of PDE, with a logistic growth rate of the prey and a general functional response of the predator. The control function has two components. The purpose is to maximize a mean density of the two species in their habitat. The existence of the optimal solution is analyzed and some necessary optimality conditions are established. The form of the optimal control is found in some particular cases.

How to cite

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Apreutesei, N. C.. "An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System." Mathematical Modelling of Natural Phenomena 5.6 (2010): 180-195. <http://eudml.org/doc/197665>.

@article{Apreutesei2010,
abstract = {An optimal control problem is studied for a predator-prey system of PDE, with a logistic growth rate of the prey and a general functional response of the predator. The control function has two components. The purpose is to maximize a mean density of the two species in their habitat. The existence of the optimal solution is analyzed and some necessary optimality conditions are established. The form of the optimal control is found in some particular cases.},
author = {Apreutesei, N. C.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {adjoint system; functional response of the predator; logistic growth rate; maximum principle; optimality conditions; functional response of predators},
language = {eng},
month = {9},
number = {6},
pages = {180-195},
publisher = {EDP Sciences},
title = {An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System},
url = {http://eudml.org/doc/197665},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Apreutesei, N. C.
TI - An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/9//
PB - EDP Sciences
VL - 5
IS - 6
SP - 180
EP - 195
AB - An optimal control problem is studied for a predator-prey system of PDE, with a logistic growth rate of the prey and a general functional response of the predator. The control function has two components. The purpose is to maximize a mean density of the two species in their habitat. The existence of the optimal solution is analyzed and some necessary optimality conditions are established. The form of the optimal control is found in some particular cases.
LA - eng
KW - adjoint system; functional response of the predator; logistic growth rate; maximum principle; optimality conditions; functional response of predators
UR - http://eudml.org/doc/197665
ER -

References

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  1. N. Apreutesei. Necessary optimality conditions for a Lotka-Volterra three species system. Math. Model. Nat. Phen., 1 (2006), 123-135. 
  2. N. Apreutesei. An optimal control problem for prey-predator system with a general functional response. Appl. Math. Letters, 22 (2009), no. 7, 1062-1065.  
  3. V. Barbu. Mathematical methods in optimization of differential systems. Kluwer Academic Publishers, Dordrecht, 1994.  
  4. G. Feichtinger , G. Tragler, V. Veliov. Optimality conditions for age-structured control systems. J. Math. Anal. Appl., 288 (2003), no. 1, 47-68.  
  5. M. Garvie, C. Trenchea. Optimal control of a nutrient-phytoplankton-zooplankton-fish system. SIAM J. Control Optim., 46 (2007), no. 3, 775-791.  
  6. Z. He, S. Hong, C. Zhang. Double control problems of age-distributed population dynamics. Nonlinear Anal., Real World Appl., 10 (2009), no. 5, 3112-3121.  
  7. I. Hrinca, An optimal control problem for the Lotka-Volterra system with diffusion. Panam. Math. J., 12 (2002), no. 3, 23-46.  
  8. N. Kato. Maximum principle for optimal harvesting in linear size-structured population. Math. Popul. Stud., 15 (2008), no. 2, 123-136.  
  9. Y. Kuang. Some mechanistically derived population models. Math. Biosci. Eng., 4 (2007), no. 4, 1-11.  
  10. J. D. Murray. Mathematical Biology. Springer Verlag, Berlin-Heidelberg-New York, third edition, 2002.  
  11. A. Pazy. Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, 44. New York etc., Springer- Verlag, 1983.  
  12. S. Xu. Existence of global solutions for a predator-prey model with cross-diffusion. Electron. J. Diff. Eqns., (2008), 1-14.  
  13. S. Yosida. Optimal control of prey-predator systems with Lagrange type and Bolza type cost functionals. Proc. Faculty Science Tokai Univ., 18 (1983), 103-118. 

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