-
1
-
-
84907774728
-
On the mathematics of the law of mass action
-
V. V. Kulkarni, G.-B. Stan, and K. Raman, eds., Springer-Verlag, London, Chapter 1
-
L. Adleman, M. Gopalkrishnan, M.-D. Huang, P. Moisset, and D. Reishus, On the mathematics of the law of mass action, in A Systems Theoretic Approach to Systems and Synthetic Biology: Models and System Characterizations, V. V. Kulkarni, G.-B. Stan, and K. Raman, eds., Springer-Verlag, London, 2014, Chapter 1.
-
(2014)
A Systems Theoretic Approach to Systems and Synthetic Biology: Models and System Characterizations
-
-
Adleman, L.1
Gopalkrishnan, M.2
Huang, M.-D.3
Moisset, P.4
Reishus, D.5
-
2
-
-
80053563926
-
Boundedness of trajectories for weakly reversible, single linkage class reaction systems
-
D. F. Anderson, Boundedness of trajectories for weakly reversible, single linkage class reaction systems, J. Math. Chem., 49 (2011), pp. 2275-2290.
-
(2011)
J. Math. Chem.
, vol.49
, pp. 2275-2290
-
-
Anderson, D.F.1
-
3
-
-
55149093414
-
Global asymptotic stability for a class of nonlinear chemical equations
-
D. F. Anderson, Global asymptotic stability for a class of nonlinear chemical equations, SIAM J. Appl. Math., 68 (2008), pp. 1464-1476.
-
(2008)
SIAM J. Appl. Math.
, vol.68
, pp. 1464-1476
-
-
Anderson, D.F.1
-
4
-
-
80052741204
-
A proof of the global attractor conjecture in the single linkage class case
-
D. F. Anderson, A proof of the global attractor conjecture in the single linkage class case, SIAM J. Appl. Math., 71 (2011), pp. 1487-1508.
-
(2011)
SIAM J. Appl. Math.
, vol.71
, pp. 1487-1508
-
-
Anderson, D.F.1
-
5
-
-
77951161620
-
The dynamics of weakly reversible population processes near facets
-
D. F. Anderson and A. Shiu, The dynamics of weakly reversible population processes near facets, SIAM J. Appl. Math., 70 (2010), pp. 1840-1858.
-
(2010)
SIAM SIAM J. Appl. Math.
, vol.70
, pp. 1840-1858
-
-
Anderson, D.F.1
Shiu, A.2
-
6
-
-
62949188295
-
On modularity and persistence of chemical reaction networks
-
IEEE Control Systems Society, Piscataway, NJ
-
D. Angeli, On modularity and persistence of chemical reaction networks, in Proceedings of the 47th IEEE Conference on Decision and Control, IEEE Control Systems Society, Piscataway, NJ, 2008, pp. 2650-2655.
-
(2008)
Proceedings of the 47th IEEE Conference on Decision and Control
, pp. 2650-2655
-
-
Angeli, D.1
-
7
-
-
67651085145
-
Chemical networks with inflows and outflows: A positive linear differential inclusions approach
-
D. Angeli, P. De Leenheer, and E. Sontag, Chemical networks with inflows and outflows: A positive linear differential inclusions approach, Biotechnol. Progr., 25 (2009), pp. 632-642.
-
(2009)
Biotechnol. Progr.
, vol.25
, pp. 632-642
-
-
Angeli, D.1
De Leenheer, P.2
Sontag, E.3
-
8
-
-
77953923165
-
Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates
-
D. Angeli, P. De Leenheer, and E. Sontag, Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates, J. Math. Biol., 61 (2010), pp. 581-616.
-
(2010)
J. Math. Biol.
, vol.61
, pp. 581-616
-
-
Angeli, D.1
De Leenheer, P.2
Sontag, E.3
-
9
-
-
79952327521
-
Persistence results for chemical reaction networks with time-dependent kinetics and no global conservation laws
-
D. Angeli, P. De Leenheer, and E. D. Sontag, Persistence results for chemical reaction networks with time-dependent kinetics and no global conservation laws, SIAM J. Appl. Math., 71 (2011), pp. 128-146.
-
(2011)
SIAM J. Appl. Math.
, vol.71
, pp. 128-146
-
-
Angeli, D.1
De Leenheer, P.2
Sontag, E.D.3
-
10
-
-
84870373872
-
Global convergence in systems of differential equations arising from chemical reaction networks
-
M. Banaji and J. Mierczynski, Global convergence in systems of differential equations arising from chemical reaction networks, J. Differential Equations, 254 (2013), pp. 1359-1374.
-
(2013)
J. Differential Equations
, vol.254
, pp. 1359-1374
-
-
Banaji, M.1
Mierczynski, J.2
-
11
-
-
0001515164
-
Maximum likelihood in three-way contingency tables
-
M. W. Birch, Maximum likelihood in three-way contingency tables, J. Roy. Stat. Soc. B Met., 25 (1963), pp. 220-233.
-
(1963)
J. Roy. Stat. Soc. B Met.
, vol.25
, pp. 220-233
-
-
Birch, M.W.1
-
13
-
-
68549135061
-
Toric dynamical systems
-
G. Craciun, A. Dickenstein, A. Shiu, and B. Sturmfels, Toric dynamical systems, J. Symbolic Comput., 44 (2009), pp. 1551-1565.
-
(2009)
J. Symbolic Comput.
, vol.44
, pp. 1551-1565
-
-
Craciun, G.1
Dickenstein, A.2
Shiu, A.3
Sturmfels, B.4
-
14
-
-
77950151527
-
Some geometrical aspects of control points for toric patches
-
Springer-Verlag, Berlin
-
G. Craciun, L. García-Puente, and F. Sottile, Some geometrical aspects of control points for toric patches, in Revised Selected Papers of the 7th International Conference on Mathematical Methods for Curves and Surfaces, Lecture Notes in Comput. Sci. 5862, Springer-Verlag, Berlin, 2010, pp. 111-135.
-
(2010)
Revised Selected Papers of the 7th International Conference on Mathematical Methods for Curves and Surfaces, Lecture Notes in Comput. Sci.
, vol.5862
, pp. 111-135
-
-
Craciun, G.1
García-Puente, L.2
Sottile, F.3
-
15
-
-
84875652420
-
Persistence and permanence of mass-action and power-law dynamical systems
-
G. Craciun, F. Nazarov, and C. Pantea, Persistence and permanence of mass-action and power-law dynamical systems, SIAM J. Appl. Math., 73 (2013), pp. 305-329.
-
(2013)
SIAM SIAM J. Appl. Math.
, vol.73
, pp. 305-329
-
-
Craciun, G.1
Nazarov, F.2
Pantea, C.3
-
16
-
-
84867885549
-
-
preprint http://arXiv.org: 1111.2386
-
J. Deng, M. Feinberg, C. Jones, and A. Nachman, On the Steady States of Weakly Reversible Chemical Reaction Networks, preprint, http://arXiv.org:1111.2386, 2011.
-
(2011)
On the Steady States of Weakly Reversible Chemical Reaction Networks
-
-
Deng, J.1
Feinberg, M.2
Jones, C.3
Nachman, A.4
-
17
-
-
84882945863
-
Local and global stability of equilibria for a class of chemical reaction networks
-
P. Donnell and M. Banaji, Local and global stability of equilibria for a class of chemical reaction networks, SIAM J. Appl. Dyn. Syst., 12 (2013), pp. 899-920.
-
(2013)
SIAM SIAM J. Appl. Dyn. Syst.
, vol.12
, pp. 899-920
-
-
Donnell, P.1
Banaji, M.2
-
18
-
-
0023531427
-
Chemical reaction network structure and the stability of complex isothermal reactors I. The deficiency zero and deficiency one theorems
-
M. Feinberg, Chemical reaction network structure and the stability of complex isothermal reactors I. The deficiency zero and deficiency one theorems, Chem. Eng. Sci., 42 (1987), pp. 2229-2268.
-
(1987)
Chem. Eng. Sci.
, vol.42
, pp. 2229-2268
-
-
Feinberg, M.1
-
19
-
-
0015482348
-
Complex balancing in general kinetic systems
-
M. Feinberg, Complex balancing in general kinetic systems, Arch. Ration. Mech. Anal., 49 (1972), pp. 187-194.
-
(1972)
Arch. Ration. Mech. Anal.
, vol.49
, pp. 187-194
-
-
Feinberg, M.1
-
20
-
-
11244254407
-
Counting stable solutions of sparse polynomial systems in chemistry
-
AMS, Providence, RI
-
K. Gatermann, Counting stable solutions of sparse polynomial systems in chemistry, in Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering (South Hadley, MA, 2000), Contemp. Math. 286, AMS, Providence, RI, 2001, pp. 53-69.
-
(2001)
Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering (South Hadley, MA 2000), Contemp. Math.
, vol.286
, pp. 53-69
-
-
Gatermann, K.1
-
21
-
-
69849107725
-
Univalent positive polynomial maps and the equilibrium state of chemical networks of reversible binding reactions
-
G. Gnacadja, Univalent positive polynomial maps and the equilibrium state of chemical networks of reversible binding reactions, Adv. in Appl. Math., 43 (2009), pp. 394-414.
-
(2009)
Adv. in Appl. Math.
, vol.43
, pp. 394-414
-
-
Gnacadja, G.1
-
22
-
-
80053561795
-
Reachability, persistence, and constructive chemical reaction networks (part III): A mathematical formalism for binary enzymatic networks and application to persistence
-
G. Gnacadja, Reachability, persistence, and constructive chemical reaction networks (part III): A mathematical formalism for binary enzymatic networks and application to persistence, J. Math. Chem., 49 (2011), pp. 2158-2176.
-
(2011)
J. Math. Chem.
, vol.49
, pp. 2158-2176
-
-
Gnacadja, G.1
-
23
-
-
85027958715
-
Catalysis in reaction networks
-
M. Gopalkrishnan, Catalysis in reaction networks, Bull. Math. Biol., 73 (2011), pp. 2962-2982.
-
(2011)
Bull. Math. Biol.
, vol.73
, pp. 2962-2982
-
-
Gopalkrishnan, M.1
-
24
-
-
84875662500
-
A projection argument for differential inclusions, with applications to persistence of mass-action kinetics
-
M. Gopalkrishnan, E. Miller, and Anne Shiu, A projection argument for differential inclusions, with applications to persistence of mass-action kinetics, SIGMA Symmetry Integrability Geom. Methods Appl., 9 (2013), 025.
-
(2013)
SIGMA Symmetry Integrability Geom. Methods Appl.
, vol.9
, pp. 025
-
-
Gopalkrishnan, M.1
Miller, E.2
Shiu, A.3
-
25
-
-
0004433445
-
The dynamics of open reaction systems
-
AMS, Providence, RI
-
F. Horn, The dynamics of open reaction systems, in Proceedings of theMathematical Aspects of Chemical and Biochemical Problems and Quantum Chemistry, SIAM-AMS Proc. 8, AMS, Providence, RI, 1974, pp. 125-137.
-
(1974)
Proceedings of TheMathematical Aspects of Chemical and Biochemical Problems and Quantum Chemistry, SIAM-AMS Proc. 8
, pp. 125-137
-
-
Horn, F.1
-
26
-
-
0015489310
-
Necessary and sufficient conditions for complex balancing in chemical kinetics
-
F. Horn, Necessary and sufficient conditions for complex balancing in chemical kinetics, Arch. Ration. Mech. Anal., 49 (1972), pp. 172-186.
-
(1972)
Arch. Ration. Mech. Anal.
, vol.49
, pp. 172-186
-
-
Horn, F.1
-
28
-
-
85027958328
-
Linear conjugacy of chemical reaction networks
-
M. D. Johnston and D. Siegel, Linear conjugacy of chemical reaction networks, J. Math. Chem., 49 (2011), pp. 1263-1282.
-
(2011)
J. Math. Chem.
, vol.49
, pp. 1263-1282
-
-
Johnston, M.D.1
Siegel, D.2
-
29
-
-
80052703942
-
Weak dynamic nonemptiability and persistence of chemical kinetics systems
-
M. D. Johnston and D. Siegel, Weak dynamic nonemptiability and persistence of chemical kinetics systems, SIAM J. Appl. Math., 71 (2011), pp. 1263-1279.
-
(2011)
SIAM SIAM J. Appl. Math.
, vol.71
, pp. 1263-1279
-
-
Johnston, M.D.1
Siegel, D.2
-
30
-
-
84897373132
-
Dynamical equivalence and linear conjugacy of chemical reaction networks: New results and methods
-
M. D. Johnston, D. Siegel, and G. Szederkényi, Dynamical equivalence and linear conjugacy of chemical reaction networks: New results and methods, MATCH Commun. Math. Comput. Chem., 68 (2012), pp. 443-468.
-
(2012)
MATCH Commun. Math. Comput. Chem.
, vol.68
, pp. 443-468
-
-
Johnston, M.D.1
Siegel, D.2
Szederkényi, G.3
-
31
-
-
0001620238
-
Analytical note on certain rhythmic relations in organic systems
-
A. J. Lotka, Analytical note on certain rhythmic relations in organic systems, Proc. Natl. Acad. Sci. USA, 6 (1920), pp. 410-415.
-
(1920)
Proc. Natl. Acad. Sci. USA
, vol.6
, pp. 410-415
-
-
Lotka, A.J.1
-
32
-
-
84923551867
-
-
Cambridge University Press, Cambridge, UK
-
S. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, 2nd ed., Cambridge University Press, Cambridge, UK, 2009.
-
(2009)
Markov Chains and Stochastic Stability, 2nd Ed
-
-
Meyn, S.1
Tweedie, R.L.2
-
33
-
-
84883634824
-
Theory and applications of lattice point methods for binomial ideals
-
Springer, Berlin, Heidelberg
-
E. Miller, Theory and applications of lattice point methods for binomial ideals, in Proceedings of the Abel Symposium on Combinatorial Aspects of Commutative Algebra and Algebraic Geometry (Voss, Norway, 2009), Abel Symposia 6, Springer, Berlin, Heidelberg, 2011, pp. 99-154.
-
(2011)
Proceedings of the Abel Symposium on Combinatorial Aspects of Commutative Algebra and Algebraic Geometry (Voss, Norway, 2009), Abel Symposia 6
, pp. 99-154
-
-
Miller, E.1
-
34
-
-
40349085795
-
Metric combinatorics of convex polyhedra: Cut loci and nonoverlapping unfoldings
-
E. Miller and I. Pak, Metric combinatorics of convex polyhedra: Cut loci and nonoverlapping unfoldings, Discrete Comput. Geom., 39 (2008), pp. 339-388.
-
(2008)
Discrete Comput. Geom.
, vol.39
, pp. 339-388
-
-
Miller, E.1
Pak, I.2
-
35
-
-
84871367577
-
Generalized mass action systems: Complex balancing equilibria and sign vectors of the stoichiometric and kinetic-order subspaces
-
S. Müller and G. Regensburger, Generalized mass action systems: Complex balancing equilibria and sign vectors of the stoichiometric and kinetic-order subspaces, SIAM J. Appl. Math., 72 (2012), pp. 1926-1947.
-
(2012)
SIAM SIAM J. Appl. Math.
, vol.72
, pp. 1926-1947
-
-
Müller, S.1
Regensburger, G.2
-
36
-
-
0003391818
-
-
Prentice Hall, Englewood Cliffs, NJ
-
J. Munkres, Topology, Prentice Hall, Englewood Cliffs, NJ, 2000.
-
(2000)
Topology
-
-
Munkres, J.1
-
38
-
-
0004237772
-
-
Cambridge University Press, Cambridge, UK
-
J. R. Norris, Markov Chains, Cambridge Series in Statistical and Probabilistic Mathematics 2, Cambridge University Press, Cambridge, UK, 1998.
-
(1998)
Cambridge Series in Statistical and Probabilistic Mathematics 2
-
-
Norris, J.R.1
Chains, M.2
-
39
-
-
84861367677
-
On the persistence and global stability of mass-action systems
-
C. Pantea, On the persistence and global stability of mass-action systems, SIAM J. Math. Anal., 44 (2012), pp. 1636-1673.
-
(2012)
SIAM SIAM J. Math. Anal.
, vol.44
, pp. 1636-1673
-
-
Pantea, C.1
-
40
-
-
0004065920
-
-
Ph.D. dissertation, Technischen Hochschule Darmstadt, Darmstadt, Germany
-
C. A. Petri, Communication with Automata, Ph.D. dissertation, Technischen Hochschule Darmstadt, Darmstadt, Germany, 1962.
-
(1962)
Communication with Automata
-
-
Petri, C.A.1
-
41
-
-
85017906175
-
Quadratic dynamical systems
-
IEEE, Washington, DC
-
Y. Rabinovich, A. Sinclair, and A. Wigderson, Quadratic dynamical systems, in Proceedings of the 33rd Annual Symposium on Foundations of Computer Science, IEEE, Washington, DC, 1992, pp. 304-313.
-
(1992)
Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
, pp. 304-313
-
-
Rabinovich, Y.1
Sinclair, A.2
Wigderson, A.3
-
42
-
-
0036628141
-
A fixed point theorem for bounded dynamical systems
-
D. Richeson and J. Wiseman, A fixed point theorem for bounded dynamical systems, Illinois J. Math., 46 (2002), pp. 491-495.
-
(2002)
Illinois J. Math.
, vol.46
, pp. 491-495
-
-
Richeson, D.1
Wiseman, J.2
-
44
-
-
84867854824
-
Concordant chemical reaction networks
-
G. Shinar and M. Feinberg, Concordant chemical reaction networks, Math Biosci., 240 (2012), pp. 92-113.
-
(2012)
Math Biosci.
, vol.240
, pp. 92-113
-
-
Shinar, G.1
Feinberg, M.2
-
45
-
-
77955170883
-
Siphons in chemical reaction networks
-
A. Shiu and B. Sturmfels, Siphons in chemical reaction networks, Bull. Math. Biol., 72 (2010), pp. 1448-1463.
-
(2010)
Bull. Math. Biol.
, vol.72
, pp. 1448-1463
-
-
Shiu, A.1
Sturmfels, B.2
-
46
-
-
79956223693
-
A stratum approach to global stability of complex balanced systems
-
D. Siegel and M. D. Johnston, A stratum approach to global stability of complex balanced systems, Dyn. Syst., 26 (2011), pp. 125-146.
-
(2011)
Dyn. Syst.
, vol.26
, pp. 125-146
-
-
Siegel, D.1
Johnston, M.D.2
-
47
-
-
0034339065
-
Global stability of complex balanced mechanisms
-
D. Siegel and D. MacLean, Global stability of complex balanced mechanisms, J. Math. Chem., 27 (2000), pp. 89-110.
-
(2000)
J. Math. Chem.
, vol.27
, pp. 89-110
-
-
Siegel, D.1
Maclean, D.2
-
48
-
-
15944405205
-
On rest points of dynamical systems
-
R. Srzednicki, On rest points of dynamical systems, Fund. Math., 126 (1985), pp. 69-81.
-
(1985)
Fund. Math.
, vol.126
, pp. 69-81
-
-
Srzednicki, R.1
-
49
-
-
79955874654
-
Finding complex balanced and detailed balanced realizations of chemical reaction networks
-
G. Szederkényi and K. M. Hangos, Finding complex balanced and detailed balanced realizations of chemical reaction networks, J. Math. Chem., 49 (2011), pp. 1163-1179.
-
(2011)
J. Math. Chem.
, vol.49
, pp. 1163-1179
-
-
Szederkényi, G.1
Hangos, K.M.2
-
50
-
-
0002142885
-
Axiomatic treatment of chemical reaction systems
-
J. Wei, Axiomatic treatment of chemical reaction systems, J. Chem. Phys., 36 (1962), pp. 1578-1584.
-
(1962)
J. Chem. Phys.
, vol.36
, pp. 1578-1584
-
-
Wei, J.1
-
51
-
-
0003222229
-
Lectures on polytopes
-
Springer-Verlag, New York
-
G. Ziegler, Lectures on Polytopes, Grad. Texts in Math. 152, Springer-Verlag, New York, 1995.
-
(1995)
Grad. Texts in Math.
, vol.152
-
-
Ziegler, G.1
|