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A detailed balanced reaction network is sufficient but not necessary for its Markov chain to be detailed balanced
1. | Dept. of Mathematics, CSU San Marcos, 333 S. Twin Oaks Valley, San Marcos, CA 92096, United States |
References:
[1] |
D. F. Anderson, G. Craciun and T. G. Kurtz, Product-form stationary distributions for deficiency zero chemical reaction networks,, Bulletin of Mathematical Biology, 72 (2010), 1947.
doi: 10.1007/s11538-010-9517-4. |
[2] |
R. Aris, Prolegomena to the rational analysis of systems of chemical reactions,, Archive for Rational Mechanics and Analysis, 19 (1965), 81.
doi: 10.1007/BF00282276. |
[3] |
R. Aris, Prolegomena to the rational analysis of systems of chemical reactions II. some addenda,, Archive for Rational Mechanics and Analysis, 27 (1968), 356.
doi: 10.1007/BF00251438. |
[4] |
H. Casimir, Some aspects of Onsager's theory of reciprocal relations in irreversible processes,, Il Nuovo Cimento, 6 (1949), 227.
doi: 10.1007/BF02780985. |
[5] |
A. Dickenstein and M. P. Millán, How far is complex balancing from detailed balancing?,, Bulletin of Mathematical Biology, 73 (2011), 811.
doi: 10.1007/s11538-010-9611-7. |
[6] |
R. Durrett, Probability: Theory and examples,, Cambridge University Press, (2010).
doi: 10.1017/CBO9780511779398. |
[7] |
M. Feinberg, Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity,, Chemical Engineering Science, 44 (1989), 1819.
doi: 10.1016/0009-2509(89)85124-3. |
[8] |
M. Feinberg, Complex balancing in general kinetic systems,, Archive for Rational Mechanics and Analysis, 49 (1972), 187.
|
[9] |
M. Feinberg, Lectures on Chemical Reaction Networks,, Notes of lectures given at the Mathematics Research Center of the University of Wisconsin in 1979, (1979). Google Scholar |
[10] |
K. Gatermann, M. Eiswirth and A. Sensse, Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems,, Journal of Symbolic Computation, 40 (2005), 1361.
doi: 10.1016/j.jsc.2005.07.002. |
[11] |
J. Gunawardena, Chemical reaction network theory for in-silico biologists,, Notes available at , (2003). Google Scholar |
[12] |
F. Horn, Necessary and sufficient conditions for complex balancing in chemical kinetics,, Archive for Rational Mechanics and Analysis, 49 (1972), 172.
|
[13] |
F. Horn and R. Jackson, General mass action kinetics,, Archive for Rational Mechanics and Analysis, 47 (1972), 81.
|
[14] |
B. Joshi, Complete characterization by multistationarity of fully open networks with one non-flow reaction,, Applied Mathematics and Computation, 219 (2013), 6931.
doi: 10.1016/j.amc.2013.01.027. |
[15] |
B. Joshi and A. Shiu, Simplifying the Jacobian Criterion for precluding multistationarity in chemical reaction networks,, SIAM Journal on Applied Mathematics, 72 (2012), 857.
doi: 10.1137/110837206. |
[16] |
B. Joshi and A. Shiu, Atoms of multistationarity in chemical reaction networks,, Journal of Mathematical Chemistry, 51 (2013), 153.
|
[17] |
B. Joshi and A. Shiu, A survey of methods for deciding whether a reaction network is multistationary,, arXiv preprint, (). Google Scholar |
[18] |
F. Kelly, Reversibility and Stochastic Networks,, Wiley, (1979).
|
[19] |
G. Lewis, A new principle of equilibrium,, Proceedings of the National Academy of Sciences of the United States of America, 11 (1925), 179.
doi: 10.1073/pnas.11.3.179. |
[20] |
L. Onsager, Reciprocal relations in irreversible processes. I,, Physical Review, 37 (1931), 405.
doi: 10.1103/PhysRev.37.405. |
[21] |
L. Paulevé, G. Craciun and H. Koeppl, Dynamical properties of discrete reaction networks,, Journal of mathematical biology, 69 (2014), 55.
doi: 10.1007/s00285-013-0686-2. |
[22] |
P. Whittle, Systems in Stochastic Equilibrium,, John Wiley & Sons, (1986).
|
[23] |
E. Wigner, Derivations of Onsager's reciprocal relations,, The Collected Works of Eugene Paul Wigner, A/4 (1997), 215.
doi: 10.1007/978-3-642-59033-7_22. |
show all references
References:
[1] |
D. F. Anderson, G. Craciun and T. G. Kurtz, Product-form stationary distributions for deficiency zero chemical reaction networks,, Bulletin of Mathematical Biology, 72 (2010), 1947.
doi: 10.1007/s11538-010-9517-4. |
[2] |
R. Aris, Prolegomena to the rational analysis of systems of chemical reactions,, Archive for Rational Mechanics and Analysis, 19 (1965), 81.
doi: 10.1007/BF00282276. |
[3] |
R. Aris, Prolegomena to the rational analysis of systems of chemical reactions II. some addenda,, Archive for Rational Mechanics and Analysis, 27 (1968), 356.
doi: 10.1007/BF00251438. |
[4] |
H. Casimir, Some aspects of Onsager's theory of reciprocal relations in irreversible processes,, Il Nuovo Cimento, 6 (1949), 227.
doi: 10.1007/BF02780985. |
[5] |
A. Dickenstein and M. P. Millán, How far is complex balancing from detailed balancing?,, Bulletin of Mathematical Biology, 73 (2011), 811.
doi: 10.1007/s11538-010-9611-7. |
[6] |
R. Durrett, Probability: Theory and examples,, Cambridge University Press, (2010).
doi: 10.1017/CBO9780511779398. |
[7] |
M. Feinberg, Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity,, Chemical Engineering Science, 44 (1989), 1819.
doi: 10.1016/0009-2509(89)85124-3. |
[8] |
M. Feinberg, Complex balancing in general kinetic systems,, Archive for Rational Mechanics and Analysis, 49 (1972), 187.
|
[9] |
M. Feinberg, Lectures on Chemical Reaction Networks,, Notes of lectures given at the Mathematics Research Center of the University of Wisconsin in 1979, (1979). Google Scholar |
[10] |
K. Gatermann, M. Eiswirth and A. Sensse, Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems,, Journal of Symbolic Computation, 40 (2005), 1361.
doi: 10.1016/j.jsc.2005.07.002. |
[11] |
J. Gunawardena, Chemical reaction network theory for in-silico biologists,, Notes available at , (2003). Google Scholar |
[12] |
F. Horn, Necessary and sufficient conditions for complex balancing in chemical kinetics,, Archive for Rational Mechanics and Analysis, 49 (1972), 172.
|
[13] |
F. Horn and R. Jackson, General mass action kinetics,, Archive for Rational Mechanics and Analysis, 47 (1972), 81.
|
[14] |
B. Joshi, Complete characterization by multistationarity of fully open networks with one non-flow reaction,, Applied Mathematics and Computation, 219 (2013), 6931.
doi: 10.1016/j.amc.2013.01.027. |
[15] |
B. Joshi and A. Shiu, Simplifying the Jacobian Criterion for precluding multistationarity in chemical reaction networks,, SIAM Journal on Applied Mathematics, 72 (2012), 857.
doi: 10.1137/110837206. |
[16] |
B. Joshi and A. Shiu, Atoms of multistationarity in chemical reaction networks,, Journal of Mathematical Chemistry, 51 (2013), 153.
|
[17] |
B. Joshi and A. Shiu, A survey of methods for deciding whether a reaction network is multistationary,, arXiv preprint, (). Google Scholar |
[18] |
F. Kelly, Reversibility and Stochastic Networks,, Wiley, (1979).
|
[19] |
G. Lewis, A new principle of equilibrium,, Proceedings of the National Academy of Sciences of the United States of America, 11 (1925), 179.
doi: 10.1073/pnas.11.3.179. |
[20] |
L. Onsager, Reciprocal relations in irreversible processes. I,, Physical Review, 37 (1931), 405.
doi: 10.1103/PhysRev.37.405. |
[21] |
L. Paulevé, G. Craciun and H. Koeppl, Dynamical properties of discrete reaction networks,, Journal of mathematical biology, 69 (2014), 55.
doi: 10.1007/s00285-013-0686-2. |
[22] |
P. Whittle, Systems in Stochastic Equilibrium,, John Wiley & Sons, (1986).
|
[23] |
E. Wigner, Derivations of Onsager's reciprocal relations,, The Collected Works of Eugene Paul Wigner, A/4 (1997), 215.
doi: 10.1007/978-3-642-59033-7_22. |
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