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Graph theory and qualitative analysis of reaction networks
1.  Zeeman Building, Mathematics Institute, University of Warwick, CV4 7AL Coventry, United Kingdom, United Kingdom 
[1] 
M. D. König, Stefano Battiston, M. Napoletano, F. Schweitzer. On algebraic graph theory and the dynamics of innovation networks. Networks & Heterogeneous Media, 2008, 3 (2) : 201219. doi: 10.3934/nhm.2008.3.201 
[2] 
Maya Mincheva, Gheorghe Craciun. Graphtheoretic conditions for zeroeigenvalue Turing instability in general chemical reaction networks. Mathematical Biosciences & Engineering, 2013, 10 (4) : 12071226. doi: 10.3934/mbe.2013.10.1207 
[3] 
Jacek Banasiak, Proscovia Namayanja. Asymptotic behaviour of flows on reducible networks. Networks & Heterogeneous Media, 2014, 9 (2) : 197216. doi: 10.3934/nhm.2014.9.197 
[4] 
Anirban Banerjee, Jürgen Jost. Spectral plot properties: Towards a qualitative classification of networks. Networks & Heterogeneous Media, 2008, 3 (2) : 395411. doi: 10.3934/nhm.2008.3.395 
[5] 
Barton E. Lee. Consensus and voting on large graphs: An application of graph limit theory. Discrete & Continuous Dynamical Systems  A, 2018, 38 (4) : 17191744. doi: 10.3934/dcds.2018071 
[6] 
Anne Shiu, Timo de Wolff. Nondegenerate multistationarity in small reaction networks. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 26832700. doi: 10.3934/dcdsb.2018270 
[7] 
Susana Merchán, Luigi Montoro, I. Peral. Optimal reaction exponent for some qualitative properties of solutions to the $p$heat equation. Communications on Pure & Applied Analysis, 2015, 14 (1) : 245268. doi: 10.3934/cpaa.2015.14.245 
[8] 
Yunfeng Jia, Yi Li, Jianhua Wu. Qualitative analysis on positive steadystates for an autocatalytic reaction model in thermodynamics. Discrete & Continuous Dynamical Systems  A, 2017, 37 (9) : 47854813. doi: 10.3934/dcds.2017206 
[9] 
Erik Kropat, Silja MeyerNieberg, GerhardWilhelm Weber. Singularly perturbed diffusionadvectionreaction processes on extremely large threedimensional curvilinear networks with a periodic microstructure  efficient solution strategies based on homogenization theory. Numerical Algebra, Control & Optimization, 2016, 6 (2) : 183219. doi: 10.3934/naco.2016008 
[10] 
Robert Carlson. Spectral theory for nonconservative transmission line networks. Networks & Heterogeneous Media, 2011, 6 (2) : 257277. doi: 10.3934/nhm.2011.6.257 
[11] 
Ivan Gentil, Bogusław Zegarlinski. Asymptotic behaviour of reversible chemical reactiondiffusion equations. Kinetic & Related Models, 2010, 3 (3) : 427444. doi: 10.3934/krm.2010.3.427 
[12] 
A. C. Eberhard, JP. Crouzeix. Existence of closed graph, maximal, cyclic pseudomonotone relations and revealed preference theory. Journal of Industrial & Management Optimization, 2007, 3 (2) : 233255. doi: 10.3934/jimo.2007.3.233 
[13] 
Serap Ergün, Bariş Bülent Kırlar, Sırma Zeynep Alparslan Gök, GerhardWilhelm Weber. An application of crypto cloud computing in social networks by cooperative game theory. Journal of Industrial & Management Optimization, 2017, 13 (5) : 115. doi: 10.3934/jimo.2019036 
[14] 
Murat Arcak, Eduardo D. Sontag. A passivitybased stability criterion for a class of biochemical reaction networks. Mathematical Biosciences & Engineering, 2008, 5 (1) : 119. doi: 10.3934/mbe.2008.5.1 
[15] 
Klemens Fellner, Wolfang Prager, Bao Q. Tang. The entropy method for reactiondiffusion systems without detailed balance: First order chemical reaction networks. Kinetic & Related Models, 2017, 10 (4) : 10551087. doi: 10.3934/krm.2017042 
[16] 
Stéphane Chrétien, Sébastien Darses, Christophe Guyeux, Paul Clarkson. On the pinning controllability of complex networks using perturbation theory of extreme singular values. application to synchronisation in power grids. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 289299. doi: 10.3934/naco.2017019 
[17] 
Casian Pantea, Heinz Koeppl, Gheorghe Craciun. Global injectivity and multiple equilibria in uni and bimolecular reaction networks. Discrete & Continuous Dynamical Systems  B, 2012, 17 (6) : 21532170. doi: 10.3934/dcdsb.2012.17.2153 
[18] 
B. Ambrosio, M. A. AzizAlaoui, V. L. E. Phan. Global attractor of complex networks of reactiondiffusion systems of FitzhughNagumo type. Discrete & Continuous Dynamical Systems  B, 2018, 23 (9) : 37873797. doi: 10.3934/dcdsb.2018077 
[19] 
Eric Babson and Dmitry N. Kozlov. Topological obstructions to graph colorings. Electronic Research Announcements, 2003, 9: 6168. 
[20] 
Oded Schramm. Hyperfinite graph limits. Electronic Research Announcements, 2008, 15: 1723. doi: 10.3934/era.2008.15.17 
2017 Impact Factor: 1.187
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