Dynamics of a plant-herbivore model with toxin-induced functional response
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1.
School of Mathematics and System Sciences & LMIB, Beihang University, Beijing, 100191
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2.
Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395
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Received:
01 June 2009
Accepted:
29 June 2018
Published:
01 January 2010
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MSC :
37C75, 37G15, 92D25.
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Traditional functional responses for plant-herbivore interactions do
not take into account explicitly the effect of plant toxin.
However, considerable evidence suggests that toxins set upper limits
on food intake for many species of herbivorous vertebrates. In this
paper, a mathematical model for plant-herbivore interactions
mediated by toxin-determined functional response is studied. The
model consists of three ordinary differential equations describing
one herbivore population and two plant species with different
toxicity levels. The effect of plant toxicity on herbivore's intake
rate is incorporated explicitly in the model by assuming an
increased handling time. The dynamical behaviors of the model are
analyzed and the results are used to examine the influence of
toxin-determined intake in the community composition of plant
species. The bifurcation analysis presented in this paper suggests
that the toxin-mediated functional response may have dramatic
effects on plant-herbivore interactions.
Citation: Ya Li, Z. Feng. Dynamics of a plant-herbivore model with toxin-induced functional response[J]. Mathematical Biosciences and Engineering, 2010, 7(1): 149-169. doi: 10.3934/mbe.2010.7.149
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Abstract
Traditional functional responses for plant-herbivore interactions do
not take into account explicitly the effect of plant toxin.
However, considerable evidence suggests that toxins set upper limits
on food intake for many species of herbivorous vertebrates. In this
paper, a mathematical model for plant-herbivore interactions
mediated by toxin-determined functional response is studied. The
model consists of three ordinary differential equations describing
one herbivore population and two plant species with different
toxicity levels. The effect of plant toxicity on herbivore's intake
rate is incorporated explicitly in the model by assuming an
increased handling time. The dynamical behaviors of the model are
analyzed and the results are used to examine the influence of
toxin-determined intake in the community composition of plant
species. The bifurcation analysis presented in this paper suggests
that the toxin-mediated functional response may have dramatic
effects on plant-herbivore interactions.
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