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Finite fluctuations and multiple steady states far from equilibrium

  • Paper from the Dissipative Structures Section of the Tenth Symposium on Biomathematics and Computer Science in the Life Sciences, University of Texas, Houston. March 29–31, 1973
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Abstract

The role of finite fluctuations in transitions between nonequilibrium steady states in nonlinear systems is investigated. Attention is focused on a model biochemical system for which the usual deterministic chemical kinetics predicts a far-from-equilibrium region of multiple steady states. A stochastic approach to chemical kinetics is adopted to study explicitly the effect of fluctuations around the coexisting stable states on a predicted hysteresis in the transition between those states. A numerical solution of the stochastic master equation for the system yields results which differ qualitatively from predictions of the purely macroscopic theory. Possible implications of these results are considered, and several important aspects of the computational scheme are discussed in some detail.

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Literature

  • Babloyantz, A. and G. Nicolis. 1972. “Chemical Instabilities and Multiple Steady State Transitions in Monod-Jacob Type Models.”J. Theor. Biology,34, 185–192.

    Article  Google Scholar 

  • Blumenthal, R., J.-P. Changeux and R. Lefever. 1970. “Membrane Excitability and Dissipative Instabilities.”J. Membrane Biol.,2, 351–374.

    Article  Google Scholar 

  • Edelstein, B. B. 1970. “Biochemical Model with Multiple Steady States and Hysteresis.”J. Theor. Biology,29, 57–62.

    Article  Google Scholar 

  • Glansdorff, P. and I. Prigogine. 1971.Thermodynamics Theory of Structure, Stability and Fluctuations. London: Wiley-Interscience.

    Google Scholar 

  • Kobatake, Y. 1970. “Transition Between Two Steady States in a Porous Charged Membrane.”Physica,48, 301–312.

    Article  Google Scholar 

  • Lefever, R. 1968. “Dissipative Structures in Chemical Systems.”J. Chem. Phys.,49, 4977–4978.

    Article  Google Scholar 

  • McQuarrie, D. A. 1967.Stochastic Approach to Chemical Kinetics. London: Methuen. Vol. 8 of Suppl. Rev. Ser. in Appl. Prob.

    Google Scholar 

  • Nicolis, G. and A. Babloyantz. 1969. “Fluctuations in Open Systems.”J. Chem. Phys.,51, 2632–2637.

    Article  Google Scholar 

  • — 1972. “Fluctuations Around Nonequilibrium States in Open Nonlinear Systems”.J. Stat. Phys.,6, 195–222.

    Article  Google Scholar 

  • Prigogine, I. and G. Nicolis. 1971. “Fluctuations in Nonequilibrium Systems.”Proc. Nat. Acad. Sci.,68, 2102–1207.

    Article  MATH  MathSciNet  Google Scholar 

  • —— and A. Babloyantz. 1972. “Thermodynamics of Evolution.”Physics Today,25, (11), 23–28; (12), 38–44.

    Article  Google Scholar 

  • Turner, J. S. 1974. “Finite Fluctuations, Nonlinear Thermodynamics, and Far-from-Equilibrium Transitions Between Multiple Steady States.” InMembranes, Dissipative Structures and Evolution. G. Nicolis and R. Lefever, Eds. Adv. Chem. Phys. (in press).

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Proceedings article from the Dissipative Structures Section of the Tenth Symposium on Biomathematics and Computer Science in the Life Sciences, University of Texas, Houston. March 29–31, 1973. Symposium Chairman: Suart O. Zimmerman. Session Chairman and Proceedings Editors: Charles Walter and Hugo M. Martinez.

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Turner, J.S. Finite fluctuations and multiple steady states far from equilibrium. Bltn Mathcal Biology 36, 205–213 (1974). https://doi.org/10.1007/BF02458604

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  • DOI: https://doi.org/10.1007/BF02458604

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