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Optimal Control for Lotka-Volterra Systems with a Hunter Population

  • Narcisa Apreutesei
  • Gabriel Dimitriu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4818)

Abstract

Of concern is an ecosystem consisting of a herbivorous species and a carnivorous one. A hunter population is introduced in the ecosystem. Suppose that it acts only on the carnivorous species and that the number of the hunted individuals is proportional to the number of the existing individuals in the carnivorous population. We find the optimal control in order to maximize the total number of individuals (prey and predators) at the end of a given time interval. Some numerical experiments are also presented.

Keywords

Optimal Control Problem Time Behavior Transversality Condition Switching Point Adjoint System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Apreutesei, N.: An optimal control problem for Lotka-Volterra system with diffusion. Bul. Inst. Polytechnic Iaşi 41(48), fasc. 1–2, 31–41 (1998)zbMATHGoogle Scholar
  2. 2.
    Apreutesei, N.: Necessary optimality conditions for a Lotka-Volterra three species system. Math. Modelling Natural Phen. 1(1), 123–135 (2006)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Barbu, V.: Mathematical Methods in Optimization of Differential Systems. Kluwer Academic Publishers, Dordrecht (1994)CrossRefzbMATHGoogle Scholar
  4. 4.
    Brauer, F., Castillo-Chavez, C.: Mathematical Models in Population Biology and Epidemiology. Springer, Berlin (2000)zbMATHGoogle Scholar
  5. 5.
    Haimovici, A.: A control problem related to a Volterra prey- predator system. In: Anal. Ştiinţ. Univ. Al. I. Cuza Iaşi, Supliment la tomul 25, s. I, pp. 33–41 (1979)Google Scholar
  6. 6.
    Haimovici, A.: A control problem for a Volterra three species system. Mathematica — Revue d’Analyse Numérique et de Théorie de l’Approx 23(46),(1) 35–41 (1980)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Murray, J.D.: Mathematical Biology, 3rd edn. Springer, Berlin (2002)zbMATHGoogle Scholar
  8. 8.
    Sussmann, H.: A bang-bang theorem with bounds on the number of switchings. SIAM J. Control Optimization 17, 629–651 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Sussmann, H.: Bounds on the number of switchings for trajectories of piecewise analytic vector fields. J. Differ. Equations 43, 399–418 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Yosida, S.: An optimal control problem of the prey-predator system. Funck. Ekvacioj 25, 283–293 (1982)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Narcisa Apreutesei
    • 1
  • Gabriel Dimitriu
    • 2
  1. 1.Department of MathematicsTechnical University “Gh. Asachi”IaşiRomania
  2. 2.Department of Mathematics and InformaticsUniversity of Medicine and Pharmacy “Gr. T. Popa”IaşiRomania

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