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Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue
Equilibria and stability analysis of a branched metabolic network with feedback inhibition
1. | Laboratoire des systèmes et signaux, Université Paris-Sud, CNRS, Supélec, 91192, Gif-sur-Yvette |
2. | INRIA Sophia-Antipolis, COMORE Project-team, 2004 route des lucioles, BP 93, 06902 Sophia-Antipolis Cedex, France |
3. | Centre for Systems Engineering and Applied Mechanics (CESAME), Université Catholique de Louvain, Bâtiment Euler, 4-6, avenue G.Lemaitre,, 1348 Louvain la Neuve, Belgium |
[1] |
Nathaniel J. Merrill, Zheming An, Sean T. McQuade, Federica Garin, Karim Azer, Ruth E. Abrams, Benedetto Piccoli. Stability of metabolic networks via Linear-in-Flux-Expressions. Networks and Heterogeneous Media, 2019, 14 (1) : 101-130. doi: 10.3934/nhm.2019006 |
[2] |
Ginestra Bianconi, Riccardo Zecchina. Viable flux distribution in metabolic networks. Networks and Heterogeneous Media, 2008, 3 (2) : 361-369. doi: 10.3934/nhm.2008.3.361 |
[3] |
Alessia Marigo. Equilibria for data networks. Networks and Heterogeneous Media, 2007, 2 (3) : 497-528. doi: 10.3934/nhm.2007.2.497 |
[4] |
Joo Sang Lee, Takashi Nishikawa, Adilson E. Motter. Why optimal states recruit fewer reactions in metabolic networks. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 2937-2950. doi: 10.3934/dcds.2012.32.2937 |
[5] |
Patrick D. Leenheer, David Angeli, Eduardo D. Sontag. On Predator-Prey Systems and Small-Gain Theorems. Mathematical Biosciences & Engineering, 2005, 2 (1) : 25-42. doi: 10.3934/mbe.2005.2.25 |
[6] |
Anne Shiu, Timo de Wolff. Nondegenerate multistationarity in small reaction networks. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2683-2700. doi: 10.3934/dcdsb.2018270 |
[7] |
Alberto Bressan, Ke Han. Existence of optima and equilibria for traffic flow on networks. Networks and Heterogeneous Media, 2013, 8 (3) : 627-648. doi: 10.3934/nhm.2013.8.627 |
[8] |
PaweŁ Hitczenko, Georgi S. Medvedev. Stability of equilibria of randomly perturbed maps. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 369-381. doi: 10.3934/dcdsb.2017017 |
[9] |
D. J. W. Simpson. On the stability of boundary equilibria in Filippov systems. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3093-3111. doi: 10.3934/cpaa.2021097 |
[10] |
G. A. Enciso, E. D. Sontag. Global attractivity, I/O monotone small-gain theorems, and biological delay systems. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 549-578. doi: 10.3934/dcds.2006.14.549 |
[11] |
Frederic Laurent-Polz, James Montaldi, Mark Roberts. Point vortices on the sphere: Stability of symmetric relative equilibria. Journal of Geometric Mechanics, 2011, 3 (4) : 439-486. doi: 10.3934/jgm.2011.3.439 |
[12] |
Paul Georgescu, Hong Zhang, Daniel Maxin. The global stability of coexisting equilibria for three models of mutualism. Mathematical Biosciences & Engineering, 2016, 13 (1) : 101-118. doi: 10.3934/mbe.2016.13.101 |
[13] |
Emiliano Cristiani, Fabio S. Priuli. A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks. Networks and Heterogeneous Media, 2015, 10 (4) : 857-876. doi: 10.3934/nhm.2015.10.857 |
[14] |
Alberto Bressan, Khai T. Nguyen. Optima and equilibria for traffic flow on networks with backward propagating queues. Networks and Heterogeneous Media, 2015, 10 (4) : 717-748. doi: 10.3934/nhm.2015.10.717 |
[15] |
Desheng Li, P.E. Kloeden. Robustness of asymptotic stability to small time delays. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 1007-1034. doi: 10.3934/dcds.2005.13.1007 |
[16] |
Ying Sue Huang, Chai Wah Wu. Stability of cellular neural network with small delays. Conference Publications, 2005, 2005 (Special) : 420-426. doi: 10.3934/proc.2005.2005.420 |
[17] |
Sílvia Cuadrado. Stability of equilibria of a predator-prey model of phenotype evolution. Mathematical Biosciences & Engineering, 2009, 6 (4) : 701-718. doi: 10.3934/mbe.2009.6.701 |
[18] |
Lyudmila Grigoryeva, Juan-Pablo Ortega, Stanislav S. Zub. Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies. Journal of Geometric Mechanics, 2014, 6 (3) : 373-415. doi: 10.3934/jgm.2014.6.373 |
[19] |
Elbaz I. Abouelmagd, Juan L. G. Guirao, Aatef Hobiny, Faris Alzahrani. Stability of equilibria points for a dumbbell satellite when the central body is oblate spheroid. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1047-1054. doi: 10.3934/dcdss.2015.8.1047 |
[20] |
Shangbing Ai. Global stability of equilibria in a tick-borne disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 567-572. doi: 10.3934/mbe.2007.4.567 |
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