Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology

0481366 - MÚ 2018 RIV CH eng M - Monography Chapter
Plesa, T. - Vejchodský, Tomáš - Erban, R.
Test Models for Statistical Inference: Two-Dimensional Reaction Systems Displaying Limit Cycle Bifurcations and Bistability.
Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology. 1. Cham: Springer, 2017 - (Holcman, D.), s. 3-27. ISBN 978-3-319-62626-0
Institutional support: RVO:67985840
Keywords : ordinary-differential equations * reaction systems * multistability
OECD category: Applied mathematics
https://link.springer.com/chapter/10.1007%2F978-3-319-62627-7_1

Theoretical results regarding two-dimensional ordinary-differential equations (ODEs) with second-degree polynomial right-hand sides are summarized, with an emphasis on limit cycles, limit cycle bifurcations and multistability. The results are then used for construction of two reaction systems, which are at the deterministic level described by two-dimensional third-degree kinetic ODEs. The first system displays a homoclinic bifurcation, and a coexistence of a stable critical point and a stable limit cycle in the phase plane. The second system displays a multiple limit cycle bifurcation, and a coexistence of two stable limit cycles. The deterministic solutions of the constructed systems are compared, and the observed differences highlighted. The constructed systems are proposed as test problems for statistical methods, which are designed to detect and classify properties of given noisy time-series arising from biological applications.
Permanent Link: http://hdl.handle.net/11104/0276940