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

top
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

top

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

top
  1. N. Apreutesei. Necessary optimality conditions for a Lotka-Volterra three species system. Math. Model. Nat. Phen., 1 (2006), 123-135. Zbl1201.92058
  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.  Zbl1179.49023
  3. V. Barbu. Mathematical methods in optimization of differential systems. Kluwer Academic Publishers, Dordrecht, 1994.  Zbl0819.49002
  4. G. Feichtinger , G. Tragler, V. Veliov. Optimality conditions for age-structured control systems. J. Math. Anal. Appl., 288 (2003), no. 1, 47-68.  Zbl1042.49035
  5. M. Garvie, C. Trenchea. Optimal control of a nutrient-phytoplankton-zooplankton-fish system. SIAM J. Control Optim., 46 (2007), no. 3, 775-791.  Zbl05288504
  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.  Zbl1162.92042
  7. I. Hrinca, An optimal control problem for the Lotka-Volterra system with diffusion. Panam. Math. J., 12 (2002), no. 3, 23-46.  Zbl1040.49003
  8. N. Kato. Maximum principle for optimal harvesting in linear size-structured population. Math. Popul. Stud., 15 (2008), no. 2, 123-136.  Zbl1166.92322
  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.  Zbl1006.92001
  11. A. Pazy. Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, 44. New York etc., Springer- Verlag, 1983.  Zbl0516.47023
  12. S. Xu. Existence of global solutions for a predator-prey model with cross-diffusion. Electron. J. Diff. Eqns., (2008), 1-14.  Zbl1138.35349
  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. Zbl0541.49003

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.