American Institute of Mathematical Sciences

Advanced
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
[1]

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
[2]

Lin Wang, James Watmough, Fang Yu. Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions. Mathematical Biosciences & Engineering, 2015, 12 (4) : 699-715. doi: 10.3934/mbe.2015.12.699
[3]

Yang Kuang, Jef Huisman, James J. Elser. Stoichiometric Plant-Herbivore Models and Their Interpretation. Mathematical Biosciences & Engineering, 2004, 1 (2) : 215-222. doi: 10.3934/mbe.2004.1.215
[4]

Jun Zhou. Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack. Mathematical Biosciences & Engineering, 2016, 13 (4) : 857-885. doi: 10.3934/mbe.2016021
[5]

Ricardo López-Ruiz, Danièle Fournier-Prunaret. Complex Behavior in a Discrete Coupled Logistic Model for the Symbiotic Interaction of Two Species. Mathematical Biosciences & Engineering, 2004, 1 (2) : 307-324. doi: 10.3934/mbe.2004.1.307
[6]

Kolade M. Owolabi, Kailash C. Patidar, Albert Shikongo. Efficient numerical method for a model arising in biological stoichiometry of tumour dynamics. Discrete & Continuous Dynamical Systems - S, 2019, 12 (3) : 591-613. doi: 10.3934/dcdss.2019038
[7]

Hui Cao, Yicang Zhou, Zhien Ma. Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1399-1417. doi: 10.3934/mbe.2013.10.1399
[8]

Yun Kang. Permanence of a general discrete-time two-species-interaction model with nonlinear per-capita growth rates. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 2123-2142. doi: 10.3934/dcdsb.2013.18.2123
[9]

Andrew L. Nevai, Richard R. Vance. The role of leaf height in plant competition for sunlight: analysis of a canopy partitioning model. Mathematical Biosciences & Engineering, 2008, 5 (1) : 101-124. doi: 10.3934/mbe.2008.5.101
[10]

Lijuan Wang, Hongling Jiang, Ying Li. Positive steady state solutions of a plant-pollinator model with diffusion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1805-1819. doi: 10.3934/dcdsb.2015.20.1805
[11]

Jesús Cuevas, Bernardo Sánchez-Rey, J. C. Eilbeck, Francis Michael Russell. Interaction of moving discrete breathers with interstitial defects. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1057-1067. doi: 10.3934/dcdss.2011.4.1057
[12]

M. R. S. Kulenović, Orlando Merino. Global bifurcation for discrete competitive systems in the plane. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 133-149. doi: 10.3934/dcdsb.2009.12.133
[13]

Robert Skiba, Nils Waterstraat. The index bundle and multiparameter bifurcation for discrete dynamical systems. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5603-5629. doi: 10.3934/dcds.2017243
[14]

Yvan Martel, Frank Merle. Inelastic interaction of nearly equal solitons for the BBM equation. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 487-532. doi: 10.3934/dcds.2010.27.487
[15]

Yang Kuang, John D. Nagy, James J. Elser. Biological stoichiometry of tumor dynamics: Mathematical models and analysis. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 221-240. doi: 10.3934/dcdsb.2004.4.221
[16]

I. D. Chueshov, Iryna Ryzhkova. A global attractor for a fluid--plate interaction model. Communications on Pure & Applied Analysis, 2013, 12 (4) : 1635-1656. doi: 10.3934/cpaa.2013.12.1635
[17]

Brandon Lindley, Qi Wang, Tianyu Zhang. A multicomponent model for biofilm-drug interaction. Discrete & Continuous Dynamical Systems - B, 2011, 15 (2) : 417-456. doi: 10.3934/dcdsb.2011.15.417
[18]

Joaquín Delgado, Eymard Hernández–López, Lucía Ivonne Hernández–Martínez. Bautin bifurcation in a minimal model of immunoediting. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1397-1414. doi: 10.3934/dcdsb.2019233
[19]

Carlos Garca-Azpeitia, Jorge Ize. Bifurcation of periodic solutions from a ring configuration of discrete nonlinear oscillators. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 975-983. doi: 10.3934/dcdss.2013.6.975
[20]

Jean-Philippe Lessard, Evelyn Sander, Thomas Wanner. Rigorous continuation of bifurcation points in the diblock copolymer equation. Journal of Computational Dynamics, 2017, 4 (1&2) : 71-118. doi: 10.3934/jcd.2017003

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences