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Open- and closed-loop equilibrium control of trophic chains

Author

Listed:
  • Gámez, M.
  • López, I.
  • Shamandy, A.

Abstract

If a nearly natural population system is deviated from its equilibrium, an important task of conservation ecology may be to control it back into equilibrium. In the paper a trophic chain is considered, and control systems are obtained by changing certain model parameters into control variables. For the equilibrium control two approaches are proposed. First, for a fixed time interval, local controllability into equilibrium is proved, and applying tools of optimal control, it is also shown how an appropriate open-loop control can be determined that actually controls the system into the equilibrium in given time. Another considered problem is to control the system to a new desired equilibrium. The problem is solved by the construction of a closed-loop control which asymptotically steers the trophic chain into this new equilibrium. In this way, actually, a controlled regime shift is realized.

Suggested Citation

  • Gámez, M. & López, I. & Shamandy, A., 2010. "Open- and closed-loop equilibrium control of trophic chains," Ecological Modelling, Elsevier, vol. 221(16), pages 1839-1846.
    • Handle: RePEc:eee:ecomod:v:221:y:2010:i:16:p:1839-1846
    DOI: 10.1016/j.ecolmodel.2010.04.011
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    References listed on IDEAS

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    1. Varga, Z., 1992. "On observability of Fisher's model of selection," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 3(1), pages 15-25.
    2. Cressman, Ross & Garay, József, 2009. "A predator–prey refuge system: Evolutionary stability in ecological systems," Theoretical Population Biology, Elsevier, vol. 76(4), pages 248-257.
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