American Institute of Mathematical Sciences

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2007, 4(1): 29-46. doi: 10.3934/mbe.2007.4.29

The dynamics of a stoichiometric plant-herbivore model and its discrete analog

Guangyu Sui 1, , Meng Fan 2, , Irakli Loladze 3, and  Yang Kuang 4,

1. 

School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, P. R., China
2. 

School of Mathematics and Statistics, and Key Laboratory for Vegetation Ecology of the Education Ministry, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024
3. 

Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, United States
4. 

Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804

Received  June 2006 Revised  July 2006 Published  November 2006

Stoichiometry-based models brought into sharp focus the importance of the nutritional quality of plant for herbivore-plant dynamics. Plant quality can dramatically affect the growth rate of the herbivores and may even lead to its extinction. These results stem from models continuous in time, which raises the question of how robust they are to time discretization. Discrete time can be more appropriate for herbivores with non-overlapping generations, annual plants, and experimental data collected periodically. We analyze a continuous stoichiometric plant-herbivore model that is mechanistically formulated in [11]. We then introduce its discrete analog and compare the dynamics of the continuous and discrete models. This discrete model includes the discrete LKE model (Loladze, Kuang and Elser (2000)) as a limiting case.
Keywords: Droop equation, stoichiometry, bifurcation., plant-herbivore interaction, discrete model.
Mathematics Subject Classification: 92D40, 34K2.
Citation: Guangyu Sui, Meng Fan, Irakli Loladze, Yang Kuang. The dynamics of a stoichiometric plant-herbivore model and its discrete analog. Mathematical Biosciences & Engineering, 2007, 4 (1) : 29-46. doi: 10.3934/mbe.2007.4.29
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