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Competing species models with an infectious disease
An improved model of t cell development in the thymus and its stability analysis
1.  Department of Mathematics and Mechanics, Applied Science College, University of Science and Technology Beijing, Beijing 100083, China 
2.  Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083 
[1] 
Alan D. Rendall. Multiple steady states in a mathematical model for interactions between T cells and macrophages. Discrete & Continuous Dynamical Systems  B, 2013, 18 (3) : 769782. doi: 10.3934/dcdsb.2013.18.769 
[2] 
Lena Noethen, Sebastian Walcher. Tikhonov's theorem and quasisteady state. Discrete & Continuous Dynamical Systems  B, 2011, 16 (3) : 945961. doi: 10.3934/dcdsb.2011.16.945 
[3] 
Wenbo Cheng, Wanbiao Ma, Songbai Guo. A class of virus dynamic model with inhibitory effect on the growth of uninfected T cells caused by infected T cells and its stability analysis. Communications on Pure & Applied Analysis, 2016, 15 (3) : 795806. doi: 10.3934/cpaa.2016.15.795 
[4] 
Stéphane Mischler, Clément Mouhot. Stability, convergence to the steady state and elastic limit for the Boltzmann equation for diffusively excited granular media. Discrete & Continuous Dynamical Systems  A, 2009, 24 (1) : 159185. doi: 10.3934/dcds.2009.24.159 
[5] 
Robert Artebrant, Aslak Tveito, Glenn T. Lines. A method for analyzing the stability of the resting state for a model of pacemaker cells surrounded by stable cells. Mathematical Biosciences & Engineering, 2010, 7 (3) : 505526. doi: 10.3934/mbe.2010.7.505 
[6] 
Serge Nicaise, Cristina Pignotti, Julie Valein. Exponential stability of the wave equation with boundary timevarying delay. Discrete & Continuous Dynamical Systems  S, 2011, 4 (3) : 693722. doi: 10.3934/dcdss.2011.4.693 
[7] 
Josef Diblík. Longtime behavior of positive solutions of a differential equation with statedependent delay. Discrete & Continuous Dynamical Systems  S, 2020, 13 (1) : 3146. doi: 10.3934/dcdss.2020002 
[8] 
István Györi, Ferenc Hartung. Exponential stability of a statedependent delay system. Discrete & Continuous Dynamical Systems  A, 2007, 18 (4) : 773791. doi: 10.3934/dcds.2007.18.773 
[9] 
LaSu Mai, Kaijun Zhang. Asymptotic stability of steady state solutions for the relativistic EulerPoisson equations. Discrete & Continuous Dynamical Systems  A, 2016, 36 (2) : 9811004. doi: 10.3934/dcds.2016.36.981 
[10] 
Meihua Wei, Jianhua Wu, Yinnian He. Steadystate solutions and stability for a cubic autocatalysis model. Communications on Pure & Applied Analysis, 2015, 14 (3) : 11471167. doi: 10.3934/cpaa.2015.14.1147 
[11] 
ClaudeMichel Brauner, Josephus Hulshof, Luca Lorenzi, Gregory I. Sivashinsky. A fully nonlinear equation for the flame front in a quasisteady combustion model. Discrete & Continuous Dynamical Systems  A, 2010, 27 (4) : 14151446. doi: 10.3934/dcds.2010.27.1415 
[12] 
WeiMing Ni, Yaping Wu, Qian Xu. The existence and stability of nontrivial steady states for SKT competition model with cross diffusion. Discrete & Continuous Dynamical Systems  A, 2014, 34 (12) : 52715298. doi: 10.3934/dcds.2014.34.5271 
[13] 
Pietro Baldi. Quasiperiodic solutions of the equation $v_{t t}  v_{x x} +v^3 = f(v)$. Discrete & Continuous Dynamical Systems  A, 2006, 15 (3) : 883903. doi: 10.3934/dcds.2006.15.883 
[14] 
Yuxiang Li. Stabilization towards the steady state for a viscous HamiltonJacobi equation. Communications on Pure & Applied Analysis, 2009, 8 (6) : 19171924. doi: 10.3934/cpaa.2009.8.1917 
[15] 
Piotr Zgliczyński. Steady state bifurcations for the KuramotoSivashinsky equation: A computer assisted proof. Journal of Computational Dynamics, 2015, 2 (1) : 95142. doi: 10.3934/jcd.2015.2.95 
[16] 
Daniel Ginsberg, Gideon Simpson. Analytical and numerical results on the positivity of steady state solutions of a thin film equation. Discrete & Continuous Dynamical Systems  B, 2013, 18 (5) : 13051321. doi: 10.3934/dcdsb.2013.18.1305 
[17] 
Samir K. Bhowmik, Dugald B. Duncan, Michael Grinfeld, Gabriel J. Lord. Finite to infinite steady state solutions, bifurcations of an integrodifferential equation. Discrete & Continuous Dynamical Systems  B, 2011, 16 (1) : 5771. doi: 10.3934/dcdsb.2011.16.57 
[18] 
Samira Boussaïd, Danielle Hilhorst, Thanh Nam Nguyen. Convergence to steady state for the solutions of a nonlocal reactiondiffusion equation. Evolution Equations & Control Theory, 2015, 4 (1) : 3959. doi: 10.3934/eect.2015.4.39 
[19] 
Yaru Xie, Genqi Xu. Exponential stability of 1d wave equation with the boundary time delay based on the interior control. Discrete & Continuous Dynamical Systems  S, 2017, 10 (3) : 557579. doi: 10.3934/dcdss.2017028 
[20] 
Eugen Stumpf. Local stability analysis of differential equations with statedependent delay. Discrete & Continuous Dynamical Systems  A, 2016, 36 (6) : 34453461. doi: 10.3934/dcds.2016.36.3445 
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