-
1
-
-
36849077107
-
A modified next reaction method for simulating chemical systems with time dependent propensities and delays
-
214107
-
Anderson, D. F., 2007. A modified next reaction method for simulating chemical systems with time dependent propensities and delays. J. Chem. Phys. 127(21), 214107.
-
(2007)
J. Chem. Phys.
, vol.127
, Issue.21
-
-
Anderson, D.F.1
-
2
-
-
55149093414
-
Global asymptotic stability for a class of nonlinear chemical equations
-
Anderson, D. F., 2008a. Global asymptotic stability for a class of nonlinear chemical equations. SIAM J. Appl. Math. 68, 1464-1476.
-
(2008)
SIAM J. Appl. Math.
, vol.68
, pp. 1464-1476
-
-
Anderson, D.F.1
-
3
-
-
42649105096
-
Incorporating postleap checks in tau-leaping
-
054103
-
Anderson, D. F., 2008b. Incorporating postleap checks in tau-leaping. J. Chem. Phys. 128(5), 054103.
-
(2008)
J. Chem. Phys.
, vol.128
, Issue.5
-
-
Anderson, D.F.1
-
4
-
-
77958511108
-
-
Anderson, D. F., Craciun, G., 2010. Reduced reaction networks and persistence of chemical systems (in preparation).
-
-
-
-
5
-
-
77951161620
-
The dynamics of weakly reversible population processes near facets
-
Anderson, D. F., Shiu, A., 2010. The dynamics of weakly reversible population processes near facets. SIAM J. Appl. Math. 70(6), 1840-1858.
-
(2010)
SIAM J. Appl. Math.
, vol.70
, Issue.6
, pp. 1840-1858
-
-
Anderson, D.F.1
Shiu, A.2
-
6
-
-
77958482662
-
-
Anderson, D. F., Ganguly, A., Kurtz, T. G., 2010. Error analysis of tau-leap simulation methods. arXiv: 0909. 4790 (submitted).
-
-
-
-
7
-
-
34548532883
-
A petri net approach to the study of persistence in chemical reaction networks
-
Angeli, D., De Leenheer, P., Sontag, E. D., 2007. A petri net approach to the study of persistence in chemical reaction networks. Math. Biosci. 210, 598-618.
-
(2007)
Math. Biosci.
, vol.210
, pp. 598-618
-
-
Angeli, D.1
de Leenheer, P.2
Sontag, E.D.3
-
8
-
-
33744775760
-
Asymptotic analysis of multiscale approximations to reaction networks
-
Ball, K., Kurtz, T. G., Popovic, L., Rempala, G., 2006. Asymptotic analysis of multiscale approximations to reaction networks. Ann. Appl. Probab. 16(4), 1925-1961.
-
(2006)
Ann. Appl. Probab.
, vol.16
, Issue.4
, pp. 1925-1961
-
-
Ball, K.1
Kurtz, T.G.2
Popovic, L.3
Rempala, G.4
-
9
-
-
31544465969
-
Efficient step size selection for the tau-leaping simulation method
-
044109
-
Cao, Y., Gillespie, D. T., Petzold, L. R., 2006. Efficient step size selection for the tau-leaping simulation method. J. Chem. Phys. 124, 044109.
-
(2006)
J. Chem. Phys.
, vol.124
-
-
Cao, Y.1
Gillespie, D.T.2
Petzold, L.R.3
-
10
-
-
0003885741
-
-
Applications of Mathematics, Stochastic Modelling and Applied Probability, New York: Springer
-
Chen, H., Yao, D. D., 2001. Fundamentals of Queueing Networks, Performance, Asymptotics and Optimization, Applications of Mathematics, Stochastic Modelling and Applied Probability, vol. 46. Springer, New York.
-
(2001)
Fundamentals of Queueing Networks, Performance, Asymptotics and Optimization
, vol.46
-
-
Chen, H.1
Yao, D.D.2
-
11
-
-
27844475135
-
Multiple equilibria in complex chemical reaction networks: I. The injectivity property
-
Craciun, G., Feinberg, M., 2005. Multiple equilibria in complex chemical reaction networks: I. The injectivity property. SIAM J. Appl. Math. 65(5), 1526-1546.
-
(2005)
SIAM J. Appl. Math.
, vol.65
, Issue.5
, pp. 1526-1546
-
-
Craciun, G.1
Feinberg, M.2
-
12
-
-
33745027709
-
Multiple equilibria in complex chemical reaction networks: II. The species-reactions graph
-
Craciun, G., Feinberg, M., 2006. Multiple equilibria in complex chemical reaction networks: II. The species-reactions graph. SIAM J. Appl. Math. 66(4), 1321-1338.
-
(2006)
SIAM J. Appl. Math.
, vol.66
, Issue.4
, pp. 1321-1338
-
-
Craciun, G.1
Feinberg, M.2
-
13
-
-
33744744785
-
Understanding bistability in complex enzyme-driven networks
-
Craciun, G., Tang, Y., Feinberg, M., 2006. Understanding bistability in complex enzyme-driven networks. Proc. Natl. Acad. Sci. USA 103(23), 8697-8702.
-
(2006)
Proc. Natl. Acad. Sci. USA
, vol.103
, Issue.23
, pp. 8697-8702
-
-
Craciun, G.1
Tang, Y.2
Feinberg, M.3
-
15
-
-
0015482348
-
Complex balancing in general kinetic systems
-
Feinberg, M., 1972. Complex balancing in general kinetic systems. Arch. Ration. Mech. Anal. 49, 187-194.
-
(1972)
Arch. Ration. Mech. Anal.
, vol.49
, pp. 187-194
-
-
Feinberg, M.1
-
16
-
-
0003834324
-
Lectures on chemical reaction networks
-
Available for download at
-
Feinberg, M., 1979. Lectures on chemical reaction networks. Delivered at the Mathematics Research Center, Univ. Wisc.-Madison. Available for download at http://www. che. eng. ohio-state. edu/~feinberg/LecturesOnReactionNetworks.
-
(1979)
Delivered at the Mathematics Research Center, Univ. Wisc.-Madison
-
-
Feinberg, M.1
-
17
-
-
0023531427
-
Chemical reaction network structure and the stability of complex isothermal reactors-I. The deficiency zero and deficiency one theorems, review article 25
-
Feinberg, M., 1987. Chemical reaction network structure and the stability of complex isothermal reactors-I. The deficiency zero and deficiency one theorems, review article 25. Chem. Eng. Sci. 42, 2229-2268.
-
(1987)
Chem. Eng. Sci.
, vol.42
, pp. 2229-2268
-
-
Feinberg, M.1
-
18
-
-
0024881071
-
Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity
-
Feinberg, M., 1989. Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity. Chem. Eng. Sci. 44(9), 1819-1827.
-
(1989)
Chem. Eng. Sci.
, vol.44
, Issue.9
, pp. 1819-1827
-
-
Feinberg, M.1
-
19
-
-
0001364051
-
Existence and uniqueness of steady states for a class of chemical reaction networks
-
Feinberg, M., 1995. Existence and uniqueness of steady states for a class of chemical reaction networks. Arch. Ration. Mech. Anal. 132, 311-370.
-
(1995)
Arch. Ration. Mech. Anal.
, vol.132
, pp. 311-370
-
-
Feinberg, M.1
-
20
-
-
21444438810
-
A stochastic analysis of first-order reaction networks
-
Gadgil, C., Lee, C. H., Othmer, H. G., 2005. A stochastic analysis of first-order reaction networks. Bull. Math. Biol. 67, 901-946.
-
(2005)
Bull. Math. Biol.
, vol.67
, pp. 901-946
-
-
Gadgil, C.1
Lee, C.H.2
Othmer, H.G.3
-
21
-
-
0001144902
-
Efficient exact stochastic simulation of chemical systems with many species and many channels
-
Gibson, M. A., Bruck, J., 2000. Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A 105, 1876-1889.
-
(2000)
J. Phys. Chem. A
, vol.105
, pp. 1876-1889
-
-
Gibson, M.A.1
Bruck, J.2
-
22
-
-
0017030517
-
A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
-
Gillespie, D. T., 1976. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403-434.
-
(1976)
J. Comput. Phys.
, vol.22
, pp. 403-434
-
-
Gillespie, D.T.1
-
23
-
-
33645429016
-
Exact stochastic simulation of coupled chemical reactions
-
Gillespie, D. T., 1977. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340-2361.
-
(1977)
J. Phys. Chem.
, vol.81
, Issue.25
, pp. 2340-2361
-
-
Gillespie, D.T.1
-
24
-
-
0035933994
-
Approximate accelerated simulation of chemically reacting systems
-
Gillespie, D. T., 2001. Approximate accelerated simulation of chemically reacting systems. J. Chem. Phys. 115(4), 1716-1733.
-
(2001)
J. Chem. Phys.
, vol.115
, Issue.4
, pp. 1716-1733
-
-
Gillespie, D.T.1
-
26
-
-
0015489310
-
Necessary and sufficient conditions for complex balancing in chemical kinetics
-
Horn, F. J. M., 1972. Necessary and sufficient conditions for complex balancing in chemical kinetics. Arch. Ration. Mech. Anal. 49(3), 172-186.
-
(1972)
Arch. Ration. Mech. Anal.
, vol.49
, Issue.3
, pp. 172-186
-
-
Horn, F.J.M.1
-
27
-
-
52949095007
-
Stability and complex balancing in mass-action systems with three complexes
-
Horn, F. J. M., 1973. Stability and complex balancing in mass-action systems with three complexes. Proc. R. Soc. A 334, 331-342.
-
(1973)
Proc. R. Soc. A
, vol.334
, pp. 331-342
-
-
Horn, F.J.M.1
-
30
-
-
0003842084
-
-
Wiley Series in Probability and Mathematical Statistics, New York: Wiley
-
Kelly, F. P., 1979. Reversibility and Stochastic Networks, Wiley Series in Probability and Mathematical Statistics. Wiley, New York.
-
(1979)
Reversibility and Stochastic Networks
-
-
Kelly, F.P.1
-
31
-
-
0001455869
-
The relationship between stochastic and deterministic models for chemical reactions
-
Kurtz, T. G., 1972. The relationship between stochastic and deterministic models for chemical reactions. J. Chem. Phys. 57(7), 2976-2978.
-
(1972)
J. Chem. Phys.
, vol.57
, Issue.7
, pp. 2976-2978
-
-
Kurtz, T.G.1
-
32
-
-
0000660738
-
Strong approximation theorems for density dependent Markov chains
-
Kurtz, T. G., 1977/1978. Strong approximation theorems for density dependent Markov chains. Stoch. Proc. Appl. 6, 223-240.
-
(1977)
Stoch. Proc. Appl.
, vol.6
, pp. 223-240
-
-
Kurtz, T.G.1
-
33
-
-
77958487408
-
-
CBMS-NSF Reg. Conf. Series in Appl. Math, Philadelphia: SIAM
-
Kurtz, T. G., 1981. Approximation of Population Processes, CBMS-NSF Reg. Conf. Series in Appl. Math., vol. 36. SIAM, Philadelphia.
-
(1981)
Approximation of Population Processes
, vol.36
-
-
Kurtz, T.G.1
-
34
-
-
0004399662
-
-
Applied Stochastic Analysis, Lecture Notes in Control and Information Sciences, Berlin: Springer
-
Kurtz, T. G., 1992. Averaging for Martingale Problems and Stochastic Approximation, Applied Stochastic Analysis, Lecture Notes in Control and Information Sciences, vol. 77, pp. 186-209. Springer, Berlin.
-
(1992)
Averaging for Martingale Problems and Stochastic Approximation
, vol.77
, pp. 186-209
-
-
Kurtz, T.G.1
-
35
-
-
34547177356
-
Stochastic fluctuations in metabolic pathways
-
Levine, E., Hwa, T., 2007. Stochastic fluctuations in metabolic pathways. Proc. Natl. Acad. Sci. USA 104(22), 9224-9229.
-
(2007)
Proc. Natl. Acad. Sci. USA
, vol.104
, Issue.22
, pp. 9224-9229
-
-
Levine, E.1
Hwa, T.2
-
36
-
-
0004242697
-
-
Applications of Mathematics (New York), New York: Springer
-
Serfozo, R., 1999. Introduction to Stochastic Networks, Applications of Mathematics (New York), vol. 44. Springer, New York.
-
(1999)
Introduction to Stochastic Networks
, vol.44
-
-
Serfozo, R.1
-
37
-
-
0035390982
-
Structure and stability of certain chemical networks and applications to the kinetic proofreading of t-cell receptor signal transduction
-
Sontag, E. D., 2001. Structure and stability of certain chemical networks and applications to the kinetic proofreading of t-cell receptor signal transduction. IEEE Trans. Autom. Control. 46(7), 1028-1047.
-
(2001)
IEEE Trans. Autom. Control.
, vol.46
, Issue.7
, pp. 1028-1047
-
-
Sontag, E.D.1
|