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Mathematical Biosciences and Engineering

2007, Volume 4, Issue 1: 29-46. doi: 10.3934/mbe.2007.4.29
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The dynamics of a stoichiometric plant-herbivore model and its discrete analog

  • 1.
    School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, P. R.
  • 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
  • 4.
    Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804
  • Received: 01 June 2006 Accepted: 29 June 2018 Published: 01 November 2006

  • MSC : 92D40, 34K20.

  • 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.

    Citation: Guangyu Sui, Meng Fan, Irakli Loladze, Yang Kuang. The dynamics of a stoichiometric plant-herbivore model and its discrete analog[J]. Mathematical Biosciences and Engineering, 2007, 4(1): 29-46. doi: 10.3934/mbe.2007.4.29

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  • 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.


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    3. E. M. Elsayed, Qamar Din, Period-doubling and Neimark–Sacker bifurcations of plant–herbivore models, 2019, 2019, 1687-1847, 10.1186/s13662-019-2200-7
    4. Qamar Din, M. Sajjad Shabbir, M. Asif Khan, Khalil Ahmad, Bifurcation analysis and chaos control for a plant–herbivore model with weak predator functional response, 2019, 13, 1751-3758, 481, 10.1080/17513758.2019.1638976
    5. Şenol KARTAL, Fark Denklem Sistemleriyle Oluşturulmuş Ot-Otçul Modelinin Çatallanma Analizi, 2018, 8, 2536-4618, 237, 10.21597/jist.407880
    6. Muhammad Sajjad Shabbir, Qamar Din, Manuel De la Sen, J. F. Gómez-Aguilar, Exploring dynamics of plant–herbivore interactions: bifurcation analysis and chaos control with Holling type-II functional response, 2024, 88, 0303-6812, 10.1007/s00285-023-02020-5
    7. Mohammed Alsubhi, Rizwan Ahmed, Ibrahim Alraddadi, Faisal Alsharif, Muhammad Imran, Stability and bifurcation analysis of a discrete-time plant-herbivore model with harvesting effect, 2024, 9, 2473-6988, 20014, 10.3934/math.2024976
    8. Qamar Din, Iqra Fareed, Nonlinear Dynamics and Bifurcation Analysis of a Discrete Plant-Herbivore System: Empirical Validation and Ecological Implications, 2025, 03784754, 10.1016/j.matcom.2025.05.026
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  • © 2007 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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