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Complex Behavior in a Discrete Coupled Logistic Model for the Symbiotic Interaction of Two Species
A General Mathematical Method for Investigating the Thymic Microenvironment, Thymocyte Development, and Immunopathogenesis
1.  Department of Pathology and laboratory Medicine, The University of Texas Medical School at Houston, Houston, TX 77030, United States, United States 
[1] 
Lisette dePillis, Trevor Caldwell, Elizabeth Sarapata, Heather Williams. Mathematical modeling of regulatory T cell effects on renal cell carcinoma treatment. Discrete & Continuous Dynamical Systems  B, 2013, 18 (4) : 915943. doi: 10.3934/dcdsb.2013.18.915 
[2] 
Guanyu Wang. The Effects of Affinity Mediated Clonal Expansion of Premigrant Thymocytes on the Periphery TCell Repertoire. Mathematical Biosciences & Engineering, 2005, 2 (1) : 153168. doi: 10.3934/mbe.2005.2.153 
[3] 
Hongjing Shi, Wanbiao Ma. An improved model of t cell development in the thymus and its stability analysis. Mathematical Biosciences & Engineering, 2006, 3 (1) : 237248. doi: 10.3934/mbe.2006.3.237 
[4] 
Eduardo IbarguenMondragon, Lourdes Esteva, Leslie ChávezGalán. A mathematical model for cellular immunology of tuberculosis. Mathematical Biosciences & Engineering, 2011, 8 (4) : 973986. doi: 10.3934/mbe.2011.8.973 
[5] 
Yueping Dong, Rinko Miyazaki, Yasuhiro Takeuchi. Mathematical modeling on helper T cells in a tumor immune system. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 5572. doi: 10.3934/dcdsb.2014.19.55 
[6] 
Amy H. Lin Erickson, Alison Wise, Stephen Fleming, Margaret Baird, Zabeen Lateef, Annette Molinaro, Miranda TebohEwungkem, Lisette dePillis. A preliminary mathematical model of skin dendritic cell trafficking and induction of T cell immunity. Discrete & Continuous Dynamical Systems  B, 2009, 12 (2) : 323336. doi: 10.3934/dcdsb.2009.12.323 
[7] 
Reihaneh Mostolizadeh, Zahra Afsharnezhad, Anna MarciniakCzochra. Mathematical model of Chimeric Antigene Receptor (CAR) T cell therapy with presence of cytokine. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 6380. doi: 10.3934/naco.2018004 
[8] 
Gennadi M. Henkin, Victor M. Polterovich. A differencedifferential analogue of the Burgers equations and some models of economic development. Discrete & Continuous Dynamical Systems  A, 1999, 5 (4) : 697728. doi: 10.3934/dcds.1999.5.697 
[9] 
Frederic Abergel, Remi Tachet. A nonlinear partial integrodifferential equation from mathematical finance. Discrete & Continuous Dynamical Systems  A, 2010, 27 (3) : 907917. doi: 10.3934/dcds.2010.27.907 
[10] 
Herbert Koch. Partial differential equations with nonEuclidean geometries. Discrete & Continuous Dynamical Systems  S, 2008, 1 (3) : 481504. doi: 10.3934/dcdss.2008.1.481 
[11] 
Wilhelm Schlag. Spectral theory and nonlinear partial differential equations: A survey. Discrete & Continuous Dynamical Systems  A, 2006, 15 (3) : 703723. doi: 10.3934/dcds.2006.15.703 
[12] 
Eugenia N. Petropoulou, Panayiotis D. Siafarikas. Polynomial solutions of linear partial differential equations. Communications on Pure & Applied Analysis, 2009, 8 (3) : 10531065. doi: 10.3934/cpaa.2009.8.1053 
[13] 
Arnulf Jentzen. Taylor expansions of solutions of stochastic partial differential equations. Discrete & Continuous Dynamical Systems  B, 2010, 14 (2) : 515557. doi: 10.3934/dcdsb.2010.14.515 
[14] 
Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (8) : 31273144. doi: 10.3934/dcdsb.2017167 
[15] 
Barbara AbrahamShrauner. Exact solutions of nonlinear partial differential equations. Discrete & Continuous Dynamical Systems  S, 2018, 11 (4) : 577582. doi: 10.3934/dcdss.2018032 
[16] 
Paul Bracken. Exterior differential systems and prolongations for three important nonlinear partial differential equations. Communications on Pure & Applied Analysis, 2011, 10 (5) : 13451360. doi: 10.3934/cpaa.2011.10.1345 
[17] 
Houssein Ayoub, Bedreddine Ainseba, Michel Langlais, Rodolphe Thiébaut. Parameters identification for a model of T cell homeostasis. Mathematical Biosciences & Engineering, 2015, 12 (5) : 917936. doi: 10.3934/mbe.2015.12.917 
[18] 
Cliburn Chan, Andrew J.T. George, Jaroslav Stark. T cell sensitivity and specificity  kinetic proofreading revisited. Discrete & Continuous Dynamical Systems  B, 2003, 3 (3) : 343360. doi: 10.3934/dcdsb.2003.3.343 
[19] 
Heiko Enderling, Alexander R.A. Anderson, Mark A.J. Chaplain, Glenn W.A. Rowe. Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology. Mathematical Biosciences & Engineering, 2006, 3 (4) : 571582. doi: 10.3934/mbe.2006.3.571 
[20] 
Rafael Potrie. Partial hyperbolicity and foliations in $\mathbb{T}^3$. Journal of Modern Dynamics, 2015, 9: 81121. doi: 10.3934/jmd.2015.9.81 
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