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Test Models for Statistical Inference: Two-Dimensional Reaction Systems Displaying Limit Cycle Bifurcations and Bistability
- Source :
- Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology ISBN: 9783319626260
- Publication Year :
- 2017
- Publisher :
- Springer International Publishing, 2017.
-
Abstract
- 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 (obtained by solving the kinetic ODEs) and stochastic solutions [noisy time-series generating by the Gillespie algorithm, and the underlying probability distributions obtained by solving the chemical master equation (CME)] 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.
- Subjects :
- 0301 basic medicine
010304 chemical physics
Phase plane
01 natural sciences
Gillespie algorithm
03 medical and health sciences
030104 developmental biology
Control theory
Limit cycle
0103 physical sciences
Master equation
Applied mathematics
Homoclinic bifurcation
Limit (mathematics)
Multistability
Bifurcation
Mathematics
Subjects
Details
- ISBN :
- 978-3-319-62626-0
- ISBNs :
- 9783319626260
- Database :
- OpenAIRE
- Journal :
- Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology ISBN: 9783319626260
- Accession number :
- edsair.doi...........95d324939b55bc1ed9796a8863416f53