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Finite-time perturbations of dynamical systems and applications to tumor therapy
Daphnia species invasion, competitive exclusion, and chaotic coexistence
1. | School of Mathematics and School of Biology, Georgia Institute of Technology, Atlanta, GA 30332-0160, United States |
2. | School of Life Sciences, Arizona State University, Tempe, AZ 85287-4501, United States, United States |
3. | Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804 |
[1] |
M. R. S. Kulenović, Orlando Merino. Competitive-exclusion versus competitive-coexistence for systems in the plane. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 1141-1156. doi: 10.3934/dcdsb.2006.6.1141 |
[2] |
Azmy S. Ackleh, Youssef M. Dib, S. R.-J. Jang. Competitive exclusion and coexistence in a nonlinear refuge-mediated selection model. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 683-698. doi: 10.3934/dcdsb.2007.7.683 |
[3] |
Yixiang Wu, Necibe Tuncer, Maia Martcheva. Coexistence and competitive exclusion in an SIS model with standard incidence and diffusion. Discrete and Continuous Dynamical Systems - B, 2017, 22 (3) : 1167-1187. doi: 10.3934/dcdsb.2017057 |
[4] |
Azmy S. Ackleh, Keng Deng, Yixiang Wu. Competitive exclusion and coexistence in a two-strain pathogen model with diffusion. Mathematical Biosciences & Engineering, 2016, 13 (1) : 1-18. doi: 10.3934/mbe.2016.13.1 |
[5] |
Dan Li, Hui Wan. Coexistence and exclusion of competitive Kolmogorov systems with semi-Markovian switching. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4145-4183. doi: 10.3934/dcds.2021032 |
[6] |
Alain Rapaport, Mario Veruete. A new proof of the competitive exclusion principle in the chemostat. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3755-3764. doi: 10.3934/dcdsb.2018314 |
[7] |
Robert Stephen Cantrell, King-Yeung Lam. Competitive exclusion in phytoplankton communities in a eutrophic water column. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 1783-1795. doi: 10.3934/dcdsb.2020361 |
[8] |
Isabel Coelho, Carlota Rebelo, Elisa Sovrano. Extinction or coexistence in periodic Kolmogorov systems of competitive type. Discrete and Continuous Dynamical Systems, 2021, 41 (12) : 5743-5764. doi: 10.3934/dcds.2021094 |
[9] |
H. L. Smith, X. Q. Zhao. Competitive exclusion in a discrete-time, size-structured chemostat model. Discrete and Continuous Dynamical Systems - B, 2001, 1 (2) : 183-191. doi: 10.3934/dcdsb.2001.1.183 |
[10] |
Azmy S. Ackleh, Linda J. S. Allen. Competitive exclusion in SIS and SIR epidemic models with total cross immunity and density-dependent host mortality. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 175-188. doi: 10.3934/dcdsb.2005.5.175 |
[11] |
Yanxia Dang, Zhipeng Qiu, Xuezhi Li. Competitive exclusion in an infection-age structured vector-host epidemic model. Mathematical Biosciences & Engineering, 2017, 14 (4) : 901-931. doi: 10.3934/mbe.2017048 |
[12] |
Benlong Xu, Hongyan Jiang. Invasion and coexistence of competition-diffusion-advection system with heterogeneous vs homogeneous resources. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4255-4266. doi: 10.3934/dcdsb.2018136 |
[13] |
Chunqing Wu, Patricia J.Y. Wong. Global asymptotical stability of the coexistence fixed point of a Ricker-type competitive model. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3255-3266. doi: 10.3934/dcdsb.2015.20.3255 |
[14] |
Charlotte Beauthier, Joseph J. Winkin, Denis Dochain. Input/state invariant LQ-optimal control: Application to competitive coexistence in a chemostat. Evolution Equations and Control Theory, 2015, 4 (2) : 143-158. doi: 10.3934/eect.2015.4.143 |
[15] |
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 |
[16] |
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 |
[17] |
Yaotang Li, Suhua Li. Exclusion sets in the Δ-type eigenvalue inclusion set for tensors. Journal of Industrial and Management Optimization, 2019, 15 (2) : 507-516. doi: 10.3934/jimo.2018054 |
[18] |
Kaifa Wang, Yang Kuang. Novel dynamics of a simple Daphnia-microparasite model with dose-dependent infection. Discrete and Continuous Dynamical Systems - S, 2011, 4 (6) : 1599-1610. doi: 10.3934/dcdss.2011.4.1599 |
[19] |
Meng Fan, Bingbing Zhang, Michael Yi Li. Mechanisms for stable coexistence in an insect community. Mathematical Biosciences & Engineering, 2010, 7 (3) : 603-622. doi: 10.3934/mbe.2010.7.603 |
[20] |
Kentarou Fujie, Akio Ito, Michael Winkler, Tomomi Yokota. Stabilization in a chemotaxis model for tumor invasion. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 151-169. doi: 10.3934/dcds.2016.36.151 |
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