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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., 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 |
[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] |
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 |
[3] |
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 |
[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] |
Xiaoqing He, Sze-Bi Hsu, Feng-Bin Wang. A periodic-parabolic Droop model for two species competition in an unstirred chemostat. Discrete and Continuous Dynamical Systems, 2020, 40 (7) : 4427-4451. doi: 10.3934/dcds.2020185 |
[6] |
Kolade M. Owolabi, Kailash C. Patidar, Albert Shikongo. Efficient numerical method for a model arising in biological stoichiometry of tumour dynamics. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 591-613. doi: 10.3934/dcdss.2019038 |
[7] |
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 |
[8] |
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 |
[9] |
Yun Kang. Permanence of a general discrete-time two-species-interaction model with nonlinear per-capita growth rates. Discrete and Continuous Dynamical Systems - B, 2013, 18 (8) : 2123-2142. doi: 10.3934/dcdsb.2013.18.2123 |
[10] |
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 |
[11] |
Lijuan Wang, Hongling Jiang, Ying Li. Positive steady state solutions of a plant-pollinator model with diffusion. Discrete and Continuous Dynamical Systems - B, 2015, 20 (6) : 1805-1819. doi: 10.3934/dcdsb.2015.20.1805 |
[12] |
Jesús Cuevas, Bernardo Sánchez-Rey, J. C. Eilbeck, Francis Michael Russell. Interaction of moving discrete breathers with interstitial defects. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1057-1067. doi: 10.3934/dcdss.2011.4.1057 |
[13] |
Claudia Totzeck. An anisotropic interaction model with collision avoidance. Kinetic and Related Models, 2020, 13 (6) : 1219-1242. doi: 10.3934/krm.2020044 |
[14] |
M. R. S. Kulenović, Orlando Merino. Global bifurcation for discrete competitive systems in the plane. Discrete and Continuous Dynamical Systems - B, 2009, 12 (1) : 133-149. doi: 10.3934/dcdsb.2009.12.133 |
[15] |
Robert Skiba, Nils Waterstraat. The index bundle and multiparameter bifurcation for discrete dynamical systems. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5603-5629. doi: 10.3934/dcds.2017243 |
[16] |
Tin Phan, Bruce Pell, Amy E. Kendig, Elizabeth T. Borer, Yang Kuang. Rich dynamics of a simple delay host-pathogen model of cell-to-cell infection for plant virus. Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : 515-539. doi: 10.3934/dcdsb.2020261 |
[17] |
Yang Kuang, John D. Nagy, James J. Elser. Biological stoichiometry of tumor dynamics: Mathematical models and analysis. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 221-240. doi: 10.3934/dcdsb.2004.4.221 |
[18] |
Yvan Martel, Frank Merle. Inelastic interaction of nearly equal solitons for the BBM equation. Discrete and Continuous Dynamical Systems, 2010, 27 (2) : 487-532. doi: 10.3934/dcds.2010.27.487 |
[19] |
José A. Carrillo, Bertram Düring, Lisa Maria Kreusser, Carola-Bibiane Schönlieb. Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics. Discrete and Continuous Dynamical Systems, 2021, 41 (8) : 3985-4012. doi: 10.3934/dcds.2021025 |
[20] |
Francesco S. Patacchini, Dejan Slepčev. The nonlocal-interaction equation near attracting manifolds. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 903-929. doi: 10.3934/dcds.2021142 |
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