Dynamics of a plant-herbivore model with toxin-induced functional response
Traditional functional responses for plant-herbivore interactions donot take into account explicitly the effect of plant toxin.However, considerable evidence suggests that toxins set upper limitson food intake for many species of herbivorous vertebrates. In thispaper, a mathematical model for plant...
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AIMS Press
2009-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.149 |
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| author | Ya Li Z. Feng |
| author_facet | Ya Li Z. Feng |
| author_sort | Ya Li |
| collection | DOAJ |
| description | Traditional functional responses for plant-herbivore interactions donot take into account explicitly the effect of plant toxin.However, considerable evidence suggests that toxins set upper limitson food intake for many species of herbivorous vertebrates. In thispaper, a mathematical model for plant-herbivore interactionsmediated by toxin-determined functional response is studied. Themodel consists of three ordinary differential equations describingone herbivore population and two plant species with differenttoxicity levels. The effect of plant toxicity on herbivore's intakerate is incorporated explicitly in the model by assuming anincreased handling time. The dynamical behaviors of the model areanalyzed and the results are used to examine the influence oftoxin-determined intake in the community composition of plantspecies. The bifurcation analysis presented in this paper suggeststhat the toxin-mediated functional response may have dramaticeffects on plant-herbivore interactions. |
| format | Article |
| id | doaj-art-f47ae58bac4c449f8128237559ab4ce2 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f47ae58bac4c449f8128237559ab4ce22025-01-24T02:00:16ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-12-017114916910.3934/mbe.2010.7.149Dynamics of a plant-herbivore model with toxin-induced functional responseYa Li0Z. Feng1School of Mathematics and System Sciences & LMIB, Beihang University, Beijing, 100191School of Mathematics and System Sciences & LMIB, Beihang University, Beijing, 100191Traditional functional responses for plant-herbivore interactions donot take into account explicitly the effect of plant toxin.However, considerable evidence suggests that toxins set upper limitson food intake for many species of herbivorous vertebrates. In thispaper, a mathematical model for plant-herbivore interactionsmediated by toxin-determined functional response is studied. Themodel consists of three ordinary differential equations describingone herbivore population and two plant species with differenttoxicity levels. The effect of plant toxicity on herbivore's intakerate is incorporated explicitly in the model by assuming anincreased handling time. The dynamical behaviors of the model areanalyzed and the results are used to examine the influence oftoxin-determined intake in the community composition of plantspecies. The bifurcation analysis presented in this paper suggeststhat the toxin-mediated functional response may have dramaticeffects on plant-herbivore interactions.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.149functional responseplanttoxicitybifurcation.coexistenceplant-herbivore modelextinction |
| spellingShingle | Ya Li Z. Feng Dynamics of a plant-herbivore model with toxin-induced functional response Mathematical Biosciences and Engineering functional response planttoxicity bifurcation. coexistence plant-herbivore model extinction |
| title | Dynamics of a plant-herbivore model with toxin-induced functional response |
| title_full | Dynamics of a plant-herbivore model with toxin-induced functional response |
| title_fullStr | Dynamics of a plant-herbivore model with toxin-induced functional response |
| title_full_unstemmed | Dynamics of a plant-herbivore model with toxin-induced functional response |
| title_short | Dynamics of a plant-herbivore model with toxin-induced functional response |
| title_sort | dynamics of a plant herbivore model with toxin induced functional response |
| topic | functional response planttoxicity bifurcation. coexistence plant-herbivore model extinction |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.149 |
| work_keys_str_mv | AT yali dynamicsofaplantherbivoremodelwithtoxininducedfunctionalresponse AT zfeng dynamicsofaplantherbivoremodelwithtoxininducedfunctionalresponse |