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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 2: 257-283. doi: 10.3934/mbe.2014.11.257
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Stability and optimal control for some classes of tritrophic systems

  • 1.
    previously at CNR, Institute of Applied Mathematics and Information Technology “Enrico Magenes”, Via E. Bassini 15, 20133 Milano
  • 2.
    CNR, Institute of Applied Mathematics and Information Technology “Enrico Magenes”, Via E. Bassini 15, 20133 Milano
  • 3.
    Department of Molecular and Translational Medicine, University of Brescia, Viale Europa 11, 25125 Brescia
  • Received: 01 November 2012 Accepted: 29 June 2018 Published: 01 October 2013

  • MSC : Primary: 37N35, 49-XX, 93D20; Secondary: 92Bxx.

  • The objective of this paper is to study an optimal resource management problem for some classes of tritrophic systems composed by autotrophic resources (plants), bottom level consumers (herbivores) and top level consumers (humans). The first class of systems we discuss are linear chains, in which biomass flows from plants to herbivores, and from herbivores to humans. In the second class of systems humans are omnivorous and hence compete with herbivores for plant resources. Finally, in the third class of systems humans are omnivorous, but the plant resources are partitioned so that humans and herbivores do not complete for the same ones. The three trophic chains are expressed as Lotka-Volterra models, which seems to be a suitable choice in contexts where there is a shortage of food for the consumers. Our model parameters are taken from the literature on agro-pastoral systems in Sub-Saharan Africa.

    Citation: Luca Galbusera, Sara Pasquali, Gianni Gilioli. Stability and optimal control for some classes of tritrophic systems[J]. Mathematical Biosciences and Engineering, 2014, 11(2): 257-283. doi: 10.3934/mbe.2014.11.257

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  • The objective of this paper is to study an optimal resource management problem for some classes of tritrophic systems composed by autotrophic resources (plants), bottom level consumers (herbivores) and top level consumers (humans). The first class of systems we discuss are linear chains, in which biomass flows from plants to herbivores, and from herbivores to humans. In the second class of systems humans are omnivorous and hence compete with herbivores for plant resources. Finally, in the third class of systems humans are omnivorous, but the plant resources are partitioned so that humans and herbivores do not complete for the same ones. The three trophic chains are expressed as Lotka-Volterra models, which seems to be a suitable choice in contexts where there is a shortage of food for the consumers. Our model parameters are taken from the literature on agro-pastoral systems in Sub-Saharan Africa.


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  • This article has been cited by:

    1. Luca Galbusera, Sara Pasquali, Analysis and constrained optimal impulsive control of a Holling-II type trophic system with two sources, 2015, 352, 00160032, 2728, 10.1016/j.jfranklin.2015.03.031
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