TY - GEN
T1 - Algebraic analysis of bifurcation and limit cycles for biological systems
AU - Niu, Wei
AU - Wang, Dongming
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/52949115347
U2 - 10.1007/978-3-540-85101-1_12
DO - 10.1007/978-3-540-85101-1_12
M3 - 会议稿件
AN - SCOPUS:52949115347
SN - 3540851003
SN - 9783540851004
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 156
EP - 171
BT - Algebraic Biology - Third International Conference, AB 2008, Proceedings
T2 - 3rd International Conference on Algebraic Biology, AB 2008
Y2 - 31 July 2008 through 2 August 2008
ER -