Algebraic analysis of bifurcation and limit cycles for biological systems. (English) Zbl 1171.92307
Horimoto, Katsuhisa (ed.) et al., Algebraic biology. Third international conference, AB 2008, Castle of Hagenberg, Austria, July 31–August 2, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-85100-4/pbk). Lecture Notes in Computer Science 5147, 156-171 (2008).
Summary: In this paper, we show how to analyze bifurcation and limit cycles for biological systems by using an algebraic approach based on triangular decomposition, Gröbner bases, discriminant varieties, real solution classification, and quantifier elimination by partial CAD. The analysis of bifurcation and limit cycles for a concrete two-dimensional system, the self-assembling micelle system with chemical sinks, is presented in detail. It is proved that this system may have a focus of order 3, from which three limit cycles can be constructed by small perturbation. The applicability of our approach is further illustrated by the construction of limit cycles for a two-dimensional Kolmogorov prey-predator system and a three-dimensional Lotka-Volterra system.
For the entire collection see [Zbl 1154.92002].
For the entire collection see [Zbl 1154.92002].
MSC:
| 92C05 | Biophysics |
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 37M20 | Computational methods for bifurcation problems in dynamical systems |
| 68W30 | Symbolic computation and algebraic computation |
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