Abstract
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.
This work has been supported by the Chinese National Key Basic Research (973) Projects 2004CB318000 and 2005CB321901/2 and the SKLSDE Project 07-003.
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Niu, W., Wang, D. (2008). Algebraic Analysis of Bifurcation and Limit Cycles for Biological Systems. In: Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. (eds) Algebraic Biology. AB 2008. Lecture Notes in Computer Science, vol 5147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85101-1_12
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DOI: https://doi.org/10.1007/978-3-540-85101-1_12
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