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Stability analysis and bifurcations in a diffusive predator-prey system
A viscoelastic model for avascular tumor growth
1. | Laboratoire de Mathématiques Appliquées, UMR6620, 24 avenue des Landais, 63177 Aubière |
2. | Mathématiques Appliquées de Bordeaux, CNRS ERS 123 et, Université Bordeaux 1, 351 cours de la libération, 33405 Talence cedex |
3. | Unité de Mathématiques Pures et Appliquées, CNRS UMR 5669, Ecole Normale Supérieure de Lyon, 69364 Lyon cedex, France |
4. | Université de Lyon 1, Ciblage Thérapeutique en Oncologie, Faculté de Médecine Lyon-Sud, Oullins, F-69921, France |
5. | Université Bordeaux 1, Institut de Mathématiques, CNRS UMMR 5251, 351 cours de la libération, 33405 Talence Cedex, France |
[1] |
Yangjin Kim, Hans G. Othmer. Hybrid models of cell and tissue dynamics in tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1141-1156. doi: 10.3934/mbe.2015.12.1141 |
[2] |
Jian-Guo Liu, Min Tang, Li Wang, Zhennan Zhou. Analysis and computation of some tumor growth models with nutrient: From cell density models to free boundary dynamics. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3011-3035. doi: 10.3934/dcdsb.2018297 |
[3] |
Shihe Xu, Yinhui Chen, Meng Bai. Analysis of a free boundary problem for avascular tumor growth with a periodic supply of nutrients. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 997-1008. doi: 10.3934/dcdsb.2016.21.997 |
[4] |
Katarzyna A. Rejniak. A Single-Cell Approach in Modeling the Dynamics of Tumor Microregions. Mathematical Biosciences & Engineering, 2005, 2 (3) : 643-655. doi: 10.3934/mbe.2005.2.643 |
[5] |
Ahuod Alsheri, Ebraheem O. Alzahrani, Asim Asiri, Mohamed M. El-Dessoky, Yang Kuang. Tumor growth dynamics with nutrient limitation and cell proliferation time delay. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3771-3782. doi: 10.3934/dcdsb.2017189 |
[6] |
Frédérique Billy, Jean Clairambault, Franck Delaunay, Céline Feillet, Natalia Robert. Age-structured cell population model to study the influence of growth factors on cell cycle dynamics. Mathematical Biosciences & Engineering, 2013, 10 (1) : 1-17. doi: 10.3934/mbe.2013.10.1 |
[7] |
Katarzyna Pichór, Ryszard Rudnicki. Applications of stochastic semigroups to cell cycle models. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2365-2381. doi: 10.3934/dcdsb.2019099 |
[8] |
Gülnihal Meral, Christian Stinner, Christina Surulescu. On a multiscale model involving cell contractivity and its effects on tumor invasion. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 189-213. doi: 10.3934/dcdsb.2015.20.189 |
[9] |
Mostafa Adimy, Fabien Crauste. Modeling and asymptotic stability of a growth factor-dependent stem cell dynamics model with distributed delay. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 19-38. doi: 10.3934/dcdsb.2007.8.19 |
[10] |
Sébastien Guisset. Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations. Kinetic and Related Models, 2020, 13 (4) : 739-758. doi: 10.3934/krm.2020025 |
[11] |
Andrea Tosin. Multiphase modeling and qualitative analysis of the growth of tumor cords. Networks and Heterogeneous Media, 2008, 3 (1) : 43-83. doi: 10.3934/nhm.2008.3.43 |
[12] |
Shinji Nakaoka, Hisashi Inaba. Demographic modeling of transient amplifying cell population growth. Mathematical Biosciences & Engineering, 2014, 11 (2) : 363-384. doi: 10.3934/mbe.2014.11.363 |
[13] |
Elena Izquierdo-Kulich, Margarita Amigó de Quesada, Carlos Manuel Pérez-Amor, Magda Lopes Texeira, José Manuel Nieto-Villar. The dynamics of tumor growth and cells pattern morphology. Mathematical Biosciences & Engineering, 2009, 6 (3) : 547-559. doi: 10.3934/mbe.2009.6.547 |
[14] |
Zejia Wang, Suzhen Xu, Huijuan Song. Stationary solutions of a free boundary problem modeling growth of angiogenesis tumor with inhibitor. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2593-2605. doi: 10.3934/dcdsb.2018129 |
[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] |
Niklas Hartung. Efficient resolution of metastatic tumor growth models by reformulation into integral equations. Discrete and Continuous Dynamical Systems - B, 2015, 20 (2) : 445-467. doi: 10.3934/dcdsb.2015.20.445 |
[17] |
Urszula Ledzewicz, James Munden, Heinz Schättler. Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 415-438. doi: 10.3934/dcdsb.2009.12.415 |
[18] |
Heikki Haario, Leonid Kalachev, Marko Laine. Reduction and identification of dynamic models. Simple example: Generic receptor model. Discrete and Continuous Dynamical Systems - B, 2013, 18 (2) : 417-435. doi: 10.3934/dcdsb.2013.18.417 |
[19] |
Mengli Hao, Ting Gao, Jinqiao Duan, Wei Xu. Non-Gaussian dynamics of a tumor growth system with immunization. Inverse Problems and Imaging, 2013, 7 (3) : 697-716. doi: 10.3934/ipi.2013.7.697 |
[20] |
Mohammad A. Tabatabai, Wayne M. Eby, Karan P. Singh, Sejong Bae. T model of growth and its application in systems of tumor-immune dynamics. Mathematical Biosciences & Engineering, 2013, 10 (3) : 925-938. doi: 10.3934/mbe.2013.10.925 |
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