### Abstract

We investigate the way in which large fluctuations in an oscillating, spatially homogeneous chemical system take place. Starting from a master equation, we study both the stationary probability density of such a system far from its limit cycle and the optimal (most probable) fluctuational paths in its space of species concentrations. The flow field of optimal fluctuational paths may contain singularities, such as switching lines. A "switching line" separates regions in the space of species concentrations that are reached, with high probability, along topologically different sorts of fluctuational paths. If an unstable focus lies inside the limit cycle, the pattern of optimal fluctuational paths is singular and self-similar near the unstable focus. In fact, a switching line spirals down to the focus. The logarithm of the stationary probability density has a self-similar singular structure near the focus as well. For a homogeneous Selkov model, we provide a numerical analysis of the pattern of optimal fluctuational paths and compare it with analytic results.

Original language | English (US) |
---|---|

Pages (from-to) | 19197-19209 |

Number of pages | 13 |

Journal | Journal of Physical Chemistry |

Volume | 100 |

Issue number | 49 |

State | Published - Dec 5 1996 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Journal of Physical Chemistry*,

*100*(49), 19197-19209.

**Singular features of large fluctuations in oscillating chemical systems.** / Dykman, M. I.; Smelyanskiy, V. N.; Maier, Robert S; Silverstein, M.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry*, vol. 100, no. 49, pp. 19197-19209.

}

TY - JOUR

T1 - Singular features of large fluctuations in oscillating chemical systems

AU - Dykman, M. I.

AU - Smelyanskiy, V. N.

AU - Maier, Robert S

AU - Silverstein, M.

PY - 1996/12/5

Y1 - 1996/12/5

N2 - We investigate the way in which large fluctuations in an oscillating, spatially homogeneous chemical system take place. Starting from a master equation, we study both the stationary probability density of such a system far from its limit cycle and the optimal (most probable) fluctuational paths in its space of species concentrations. The flow field of optimal fluctuational paths may contain singularities, such as switching lines. A "switching line" separates regions in the space of species concentrations that are reached, with high probability, along topologically different sorts of fluctuational paths. If an unstable focus lies inside the limit cycle, the pattern of optimal fluctuational paths is singular and self-similar near the unstable focus. In fact, a switching line spirals down to the focus. The logarithm of the stationary probability density has a self-similar singular structure near the focus as well. For a homogeneous Selkov model, we provide a numerical analysis of the pattern of optimal fluctuational paths and compare it with analytic results.

AB - We investigate the way in which large fluctuations in an oscillating, spatially homogeneous chemical system take place. Starting from a master equation, we study both the stationary probability density of such a system far from its limit cycle and the optimal (most probable) fluctuational paths in its space of species concentrations. The flow field of optimal fluctuational paths may contain singularities, such as switching lines. A "switching line" separates regions in the space of species concentrations that are reached, with high probability, along topologically different sorts of fluctuational paths. If an unstable focus lies inside the limit cycle, the pattern of optimal fluctuational paths is singular and self-similar near the unstable focus. In fact, a switching line spirals down to the focus. The logarithm of the stationary probability density has a self-similar singular structure near the focus as well. For a homogeneous Selkov model, we provide a numerical analysis of the pattern of optimal fluctuational paths and compare it with analytic results.

UR - http://www.scopus.com/inward/record.url?scp=7344224041&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=7344224041&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:7344224041

VL - 100

SP - 19197

EP - 19209

JO - Journal of Physical Chemistry

JF - Journal of Physical Chemistry

SN - 0022-3654

IS - 49

ER -