American Institute of Mathematical Sciences

Advanced
2010, 7(1): 149-169. doi: 10.3934/mbe.2010.7.149

Dynamics of a plant-herbivore model with toxin-induced functional response

Ya Li 1, and  Z. Feng 2,

1. 

School of Mathematics and System Sciences & LMIB, Beihang University, Beijing, 100191, China
2. 

Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395

Received  June 2009 Revised  September 2009 Published  January 2010

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.
Keywords: functional response, plant toxicity, bifurcation., coexistence, plant-herbivore model, extinction.
Mathematics Subject Classification: 37C75, 37G15, 92D2.
Citation: Ya Li, Z. Feng. Dynamics of a plant-herbivore model with toxin-induced functional response. Mathematical Biosciences & Engineering, 2010, 7 (1) : 149-169. doi: 10.3934/mbe.2010.7.149
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