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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), 1947-1970.
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), 81-99.
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), 356-364.
doi: 10.1007/BF00251438. |
[4] |
H. Casimir, Some aspects of Onsager's theory of reciprocal relations in irreversible processes, Il Nuovo Cimento, 6 (1949), 227-231.
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), 811-828.
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), 1819-1827.
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), 187-194. |
[9] |
M. Feinberg, Lectures on Chemical Reaction Networks, Notes of lectures given at the Mathematics Research Center of the University of Wisconsin in 1979, available at http://www.crnt.osu.edu/LecturesOnReactionNetworks, 1979. |
[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), 1361-1382.
doi: 10.1016/j.jsc.2005.07.002. |
[11] |
J. Gunawardena, Chemical reaction network theory for in-silico biologists, Notes available at http://vcp.med.harvard.edu/papers/crnt.pdf, 2003. |
[12] |
F. Horn, Necessary and sufficient conditions for complex balancing in chemical kinetics, Archive for Rational Mechanics and Analysis, 49 (1972), 172-186. |
[13] |
F. Horn and R. Jackson, General mass action kinetics, Archive for Rational Mechanics and Analysis, 47 (1972), 81-116. |
[14] |
B. Joshi, Complete characterization by multistationarity of fully open networks with one non-flow reaction, Applied Mathematics and Computation, 219 (2013), 6931-6945.
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), 857-876.
doi: 10.1137/110837206. |
[16] |
B. Joshi and A. Shiu, Atoms of multistationarity in chemical reaction networks, Journal of Mathematical Chemistry, 51 (2013), 153-178. |
[17] |
B. Joshi and A. Shiu, A survey of methods for deciding whether a reaction network is multistationary,, arXiv preprint, ().
|
[18] |
F. Kelly, Reversibility and Stochastic Networks, Wiley, Chichester, 1979. |
[19] |
G. Lewis, A new principle of equilibrium, Proceedings of the National Academy of Sciences of the United States of America, 11 (1925), 179-183.
doi: 10.1073/pnas.11.3.179. |
[20] |
L. Onsager, Reciprocal relations in irreversible processes. I, Physical Review, 37 (1931), 405-426.
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), 55-72.
doi: 10.1007/s00285-013-0686-2. |
[22] |
P. Whittle, Systems in Stochastic Equilibrium, John Wiley & Sons, Inc., 1986. |
[23] |
E. Wigner, Derivations of Onsager's reciprocal relations, The Collected Works of Eugene Paul Wigner, A/4 (1997), 215-218.
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), 1947-1970.
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), 81-99.
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), 356-364.
doi: 10.1007/BF00251438. |
[4] |
H. Casimir, Some aspects of Onsager's theory of reciprocal relations in irreversible processes, Il Nuovo Cimento, 6 (1949), 227-231.
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), 811-828.
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), 1819-1827.
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), 187-194. |
[9] |
M. Feinberg, Lectures on Chemical Reaction Networks, Notes of lectures given at the Mathematics Research Center of the University of Wisconsin in 1979, available at http://www.crnt.osu.edu/LecturesOnReactionNetworks, 1979. |
[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), 1361-1382.
doi: 10.1016/j.jsc.2005.07.002. |
[11] |
J. Gunawardena, Chemical reaction network theory for in-silico biologists, Notes available at http://vcp.med.harvard.edu/papers/crnt.pdf, 2003. |
[12] |
F. Horn, Necessary and sufficient conditions for complex balancing in chemical kinetics, Archive for Rational Mechanics and Analysis, 49 (1972), 172-186. |
[13] |
F. Horn and R. Jackson, General mass action kinetics, Archive for Rational Mechanics and Analysis, 47 (1972), 81-116. |
[14] |
B. Joshi, Complete characterization by multistationarity of fully open networks with one non-flow reaction, Applied Mathematics and Computation, 219 (2013), 6931-6945.
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), 857-876.
doi: 10.1137/110837206. |
[16] |
B. Joshi and A. Shiu, Atoms of multistationarity in chemical reaction networks, Journal of Mathematical Chemistry, 51 (2013), 153-178. |
[17] |
B. Joshi and A. Shiu, A survey of methods for deciding whether a reaction network is multistationary,, arXiv preprint, ().
|
[18] |
F. Kelly, Reversibility and Stochastic Networks, Wiley, Chichester, 1979. |
[19] |
G. Lewis, A new principle of equilibrium, Proceedings of the National Academy of Sciences of the United States of America, 11 (1925), 179-183.
doi: 10.1073/pnas.11.3.179. |
[20] |
L. Onsager, Reciprocal relations in irreversible processes. I, Physical Review, 37 (1931), 405-426.
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), 55-72.
doi: 10.1007/s00285-013-0686-2. |
[22] |
P. Whittle, Systems in Stochastic Equilibrium, John Wiley & Sons, Inc., 1986. |
[23] |
E. Wigner, Derivations of Onsager's reciprocal relations, The Collected Works of Eugene Paul Wigner, A/4 (1997), 215-218.
doi: 10.1007/978-3-642-59033-7_22. |
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