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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 5&6: 1519-1538. doi: 10.3934/mbe.2013.10.1519
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Spatially heterogeneous invasion of toxic plant mediated by herbivory

  • 1.
    Department of Mathematics, Nanjing University of Information Science and Technology, Nanjing 210044
  • 2.
    Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899
  • 3.
    Department of Biology, University of Miami, Coral Gables, Florida 33124
  • Published: 01 August 2013

  • MSC : Primary: 92D40, 34D, 35K; Secondary: 35C07.

  • Spatially homogeneous (ODE) and  reaction-diffusion models for plant-herbivore interactions with toxin-determined functional response are analyzed. The models include two plant species that have different levels of toxicity. The plant species with a higher level of toxicity is assumed to be less preferred by the herbivore and to have a relatively lower intrinsic growth rate than the less toxic plant species. Two of the equilibrium points of the system representing significant ecological interests are $E_1$, in which only the less toxic plant is present, and$E_2$, in which the more toxic plant and herbivore coexist while the less toxic plant has gone to extinction. Under certain conditions it is shown that, for the spatially homogeneous system all solutions will converge to the equilibrium $E_2$, whereas for the reaction-diffusion model there exist  traveling wave solutions connecting  $E_1$ and $E_2$.

    Citation: Zhilan Feng, Wenzhang Huang, Donald L. DeAngelis. Spatially heterogeneous invasion of toxic plant mediated by herbivory[J]. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1519-1538. doi: 10.3934/mbe.2013.10.1519

    Related Papers:

  • Spatially homogeneous (ODE) and  reaction-diffusion models for plant-herbivore interactions with toxin-determined functional response are analyzed. The models include two plant species that have different levels of toxicity. The plant species with a higher level of toxicity is assumed to be less preferred by the herbivore and to have a relatively lower intrinsic growth rate than the less toxic plant species. Two of the equilibrium points of the system representing significant ecological interests are $E_1$, in which only the less toxic plant is present, and$E_2$, in which the more toxic plant and herbivore coexist while the less toxic plant has gone to extinction. Under certain conditions it is shown that, for the spatially homogeneous system all solutions will converge to the equilibrium $E_2$, whereas for the reaction-diffusion model there exist  traveling wave solutions connecting  $E_1$ and $E_2$.



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  • © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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