Becker, Lara ; Mendler, Marc ; Drossel, Barbara (2020)
Relation between the convective field and the stationary probability distribution of chemical reaction networks.
In: New Journal of Physics, 22 (3)
doi: 10.1088/1367-2630/ab73c6
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
We investigate the relation between the stationary probability distribution of chemical reaction systems and the convective field derived from the chemical Fokker–Planck equation (CFPE) by comparing predictions of the convective field to the results of stochastic simulations based on Gillespie's algorithm. The convective field takes into account the drift term of the CFPE and the reaction bias introduced by the diffusion term. For one-dimensional systems, fixed points and bifurcations of the convective field correspond to extrema and phenomenological bifurcations of the stationary probability distribution whenever the CFPE is a good approximation to the stochastic dynamics. This provides an efficient way to calculate the effect of system size on the number and location of probability maxima and their phenomenological bifurcations in parameter space. For two-dimensional systems, we study models that have saddle-node and Hopf bifurcations in the macroscopic limit. Here, the existence of two stable fixed points of the convective field correlates either with two peaks of the stationary probability distribution, or with a peak and a shoulder. In contrast, a Hopf bifurcation that occurs in the convective field for decreasing system size is not accompanied by the onset of a crater-shaped probability distribution; decreasing system size rather destroys craters and replaces them by local maxima.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2020 |
| Autor(en): | Becker, Lara ; Mendler, Marc ; Drossel, Barbara |
| Art des Eintrags: | Bibliographie |
| Titel: | Relation between the convective field and the stationary probability distribution of chemical reaction networks |
| Sprache: | Englisch |
| Publikationsjahr: | 10 März 2020 |
| Verlag: | IOP Publishing |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | New Journal of Physics |
| Jahrgang/Volume einer Zeitschrift: | 22 |
| (Heft-)Nummer: | 3 |
| DOI: | 10.1088/1367-2630/ab73c6 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | We investigate the relation between the stationary probability distribution of chemical reaction systems and the convective field derived from the chemical Fokker–Planck equation (CFPE) by comparing predictions of the convective field to the results of stochastic simulations based on Gillespie's algorithm. The convective field takes into account the drift term of the CFPE and the reaction bias introduced by the diffusion term. For one-dimensional systems, fixed points and bifurcations of the convective field correspond to extrema and phenomenological bifurcations of the stationary probability distribution whenever the CFPE is a good approximation to the stochastic dynamics. This provides an efficient way to calculate the effect of system size on the number and location of probability maxima and their phenomenological bifurcations in parameter space. For two-dimensional systems, we study models that have saddle-node and Hopf bifurcations in the macroscopic limit. Here, the existence of two stable fixed points of the convective field correlates either with two peaks of the stationary probability distribution, or with a peak and a shoulder. In contrast, a Hopf bifurcation that occurs in the convective field for decreasing system size is not accompanied by the onset of a crater-shaped probability distribution; decreasing system size rather destroys craters and replaces them by local maxima. |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 530 Physik |
| Fachbereich(e)/-gebiet(e): | 05 Fachbereich Physik 05 Fachbereich Physik > Institut für Festkörperphysik (2021 umbenannt in Institut für Physik Kondensierter Materie (IPKM)) 05 Fachbereich Physik > Institut für Festkörperphysik (2021 umbenannt in Institut für Physik Kondensierter Materie (IPKM)) > Statistische Physik und komplexe Systeme |
| Hinterlegungsdatum: | 29 Mär 2020 19:57 |
| Letzte Änderung: | 24 Mai 2023 08:06 |
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