Bifurcation Analysis of a Mitotic Model of Frog Eggs

Lü Jin-hu; ZHANG Zi-fan; ZHANG Suo-chun

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(3): 253-266

Lü Jin-hu, ZHANG Zi-fan, ZHANG Suo-chun. Bifurcation Analysis of a Mitotic Model of Frog Eggs[J]. Applied Mathematics and Mechanics, 2003, 24(3): 253-266.

Citation:

Lü Jin-hu, ZHANG Zi-fan, ZHANG Suo-chun. Bifurcation Analysis of a Mitotic Model of Frog Eggs[J]. Applied Mathematics and Mechanics, 2003, 24(3): 253-266.

Citation:

Lü Jin-hu, ZHANG Zi-fan, ZHANG Suo-chun. Bifurcation Analysis of a Mitotic Model of Frog Eggs[J]. Applied Mathematics and Mechanics, 2003, 24(3): 253-266.

PDF( 528 KB)

Bifurcation Analysis of a Mitotic Model of Frog Eggs

1.
Institute of Systems Science, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China;
2.
Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China

Received Date: 2001-05-18
Rev Recd Date: 2002-10-19
Publish Date: 2003-03-15

Abstract

Abstract

The mitotic model of frog eggs established by Borisuk and Tyson is qualitatively analyzed.The existence and stability of its steady states are further discussed.Furthermore, the bifurcation of above model is further investigated by using theoretical analysis and numerical simulations.At the same time, the numerical results of Tyson are verified by theoretical analysis.
- mitosis,
- steady state,
- periodic solution,
- supercritical bifurcation,
- subcritical bifurcation

FullText(HTML)

References(9)

References

[1]	Borisuk M T,Tyson J J.Bifurcation analysis of a model of mitotic control in frog eggs[J].Journal of Theoretical Biology,1998,195(1):69-85.
[2]	Novak B,Tyson J J.Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos[J].Journal of Cell Science,1993,106(4):1153-1168.
[3]	Novak B,Tyson J J.Modeling the cell division cycle:M-phase trigger,oscillations,and size control[J].Journal of Theoretical Biology,1993,165(1):101-134.
[4]	ZHENG Zuo-huan,ZHOU Tian-shou,ZHANG Suo-chun.Dynamical behavior in the modeling of cell division cycle[J].Chaos,Solitons & Fractals,2000,11(4):2371-2378.
[5]	冯贝叶,曾宪武.蛙卵有丝分裂模型的定性分析[J].应用数学学报,2002,25(3):460-468.
[6]	ZHANG Suo-chun.Oregonator:General results of positive steady state and its stability[J].Chinese Science Bulletin,1996,41(10):798-804.
[7]	张锁春.现代振荡反应的数学理论和数值方法[M].郑洲:河南科学技术出版社,1991.
[8]	张锦炎,冯贝叶.常微分方程几何理论与分支问题[M].北京:北京大学出版社,2000.
[9]	Hassard B D,Kazarinoff N D,Wan Y H.Theory and Application of Hopf Bifurcation[M].England:Cambridge University Press,1981.