English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We derive methods for estimating the topology of the stationary probabilitycurrent $\vec{j}_s$ of the two-species Fokker-Planck equation (FPE) without theneed to solve the FPE. These methods are chosen such that they become exact incertain limits, such as infinite system size or vanishing coupling betweenspecies in the diffusion matrix. The methods make predictions about the fixedpoints of $\vec{j}_s$ and their relation to extrema of the stationaryprobability distribution and to fixed points of the convective field, which isrelated to the deterministic drift of the system. Furthermore, they predict therotation sense of $\vec{j}_s$ around extrema of the stationary probabilitydistribution. Even though these methods cannot be proven to be valid away fromextrema, the boundary lines between regions with different rotation sense areobtained with surprising accuracy. We illustrate and test these method usingsimple reaction systems with only one coupling term between the two species aswell as a few generic reaction networks taken from literature. We use it alsoto investigate the shape of non-physical probability currents occurring inreaction systems with detailed balance due to the approximations involved inderiving the Fokker-Planck equation.

Predicting properties of the stationary probability currents for two-species reaction systems without solving the Fokker-Planck equation