Algebraic analysis of bifurcation and limit cycles for biological systems

Wei Niu; Dongming Wang

doi:10.1007/978-3-540-85101-1_12

Algebraic analysis of bifurcation and limit cycles for biological systems

Wei Niu^*
, Dongming Wang

^*Corresponding author for this work

School of Artificial Intelligence(Institute of Artificial Intelligence)

Laboratoire d'Informatique de Paris 6

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

11 Scopus citations

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.

Original language	English
Title of host publication	Algebraic Biology - Third International Conference, AB 2008, Proceedings
Pages	156-171
Number of pages	16
DOIs	https://doi.org/10.1007/978-3-540-85101-1_12
State	Published - 2008
Event	3rd International Conference on Algebraic Biology, AB 2008 - Castle of Hagenberg, Austria Duration: 31 Jul 2008 → 2 Aug 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5147 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Conference on Algebraic Biology, AB 2008
Country/Territory	Austria
City	Castle of Hagenberg
Period	31/07/08 → 2/08/08

Access to Document

10.1007/978-3-540-85101-1_12

Cite this

Niu, W., & Wang, D. (2008). Algebraic analysis of bifurcation and limit cycles for biological systems. In Algebraic Biology - Third International Conference, AB 2008, Proceedings (pp. 156-171). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5147 LNCS). https://doi.org/10.1007/978-3-540-85101-1_12

@inproceedings{9ea2146a2d8640d581a78bc21a840b25,

title = "Algebraic analysis of bifurcation and limit cycles for biological systems",

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, Gr{\"o}bner 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.",

author = "Wei Niu and Dongming Wang",

year = "2008",

doi = "10.1007/978-3-540-85101-1\_12",

language = "英语",

isbn = "3540851003",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "156--171",

booktitle = "Algebraic Biology - Third International Conference, AB 2008, Proceedings",

note = "3rd International Conference on Algebraic Biology, AB 2008 ; Conference date: 31-07-2008 Through 02-08-2008",

}

Niu, W & Wang, D 2008, Algebraic analysis of bifurcation and limit cycles for biological systems. in Algebraic Biology - Third International Conference, AB 2008, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5147 LNCS, pp. 156-171, 3rd International Conference on Algebraic Biology, AB 2008, Castle of Hagenberg, Austria, 31/07/08. https://doi.org/10.1007/978-3-540-85101-1_12

Algebraic analysis of bifurcation and limit cycles for biological systems. / Niu, Wei ; Wang, Dongming.
Algebraic Biology - Third International Conference, AB 2008, Proceedings. 2008. p. 156-171 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5147 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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 -

Algebraic analysis of bifurcation and limit cycles for biological systems

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this