Existence of Closed Orbits for a Differential Equation Model Concerning Multi-Molecule Reactions

Zhang Wei-nian

Volume 14 Issue 6

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1993 > 14(6): 559-566

Zhang Wei-nian. Existence of Closed Orbits for a Differential Equation Model Concerning Multi-Molecule Reactions[J]. Applied Mathematics and Mechanics, 1993, 14(6): 559-566.

Citation:

Zhang Wei-nian. Existence of Closed Orbits for a Differential Equation Model Concerning Multi-Molecule Reactions[J]. Applied Mathematics and Mechanics, 1993, 14(6): 559-566.

Citation:

Zhang Wei-nian. Existence of Closed Orbits for a Differential Equation Model Concerning Multi-Molecule Reactions[J]. Applied Mathematics and Mechanics, 1993, 14(6): 559-566.

PDF( 432 KB)

Existence of Closed Orbits for a Differential Equation Model Concerning Multi-Molecule Reactions

Zhang Wei-nian

Centre for Mathematical Sciences, Chengdu Institute of Computer Applications, Academia Sinica, Chengdu

Received Date: 1992-05-30
Publish Date: 1993-06-15

Abstract

Abstract

In this paper, the existence of closed orbits for the biochemical reaction model dx/dt=1-xⁿy²,dy/dt=a(xⁿy²-y) is discussed, where n is a positive integer and x≥0,y≥0,a>0 We also point out that the equation has no dosed orbits or has stable limit cycles arising from Hopf bifurcations under a certain condition of a.
- closed orbit,
- limit cycle,
- fine focus,
- Hopf bifurcation

FullText(HTML)

References(4)

References

[1]	陈兰荪,《数学生态学的理论和方法》,科学出版社〔1988).
[2]	周建莹、张锦炎、曾宪武,生化反应中一类非线性方程的定性分析,应用数学学报,5(3)(1982),234-240.
[3]	李嘉旭、范弘毅、姜天来、陈秀东,一类多分子反应微分方程模型的定性分析,生物数学学报,5(2)(1990),182-170.
[4]	张锦炎,《常微分方程几何理论与分支问题》,北京大学出版社(1981).

Relative Articles

[1]	GU Jieping, HUANG Wentao, CHEN Ting. Solitary Periodic Waves and Local Bifurcations of Critical Periods for a Class of Reaction-Diffusion Equations[J]. Applied Mathematics and Mechanics, 2021, 42(2): 221-232. doi: 10.21656/1000-0887.410263
[2]	LI Jiaorui, ZHANG Yanxia. Dynamic Cycle Analysis of a Solow Model With Time Delays[J]. Applied Mathematics and Mechanics, 2018, 39(3): 334-342. doi: 10.21656/1000-0887.380184
[3]	CHEN Heng, WANG Yang-yu, JIN Jiang-ming. Flutter Characteristics Analysis of 2D Rigid Airfoils With Control Surface Based on the Arc-Length Numerical Continuation Method[J]. Applied Mathematics and Mechanics, 2017, 38(7): 769-779. doi: 10.21656/1000-0887.370223
[4]	FENG Zhi-peng, ZHANG Yi-xiong, ZANG Feng-gang, YE Xian-hui. Analysis of Vortex-Induced Vibration Characteristics for a Three Dimensional Flexible Tube[J]. Applied Mathematics and Mechanics, 2013, 34(9): 976-985. doi: 10.3879/j.issn.1000-0887.2013.09.011
[5]	GUO Hu-lun, CHEN Yu-shu. Dynamic Analysis of a Two-Degree-of-Freedom Airfoil With Freeplay and Cubic Nonlinearities in Supersonic Flow[J]. Applied Mathematics and Mechanics, 2012, 33(1): 1-13. doi: 10.3879/j.issn.1000-0887.2012.01.001
[6]	HUANG Cheng-biao, LIU Jia. Limit Cycles and Homoclinic Orbits and Their Bifurcation of the Bogdanov-Takens System[J]. Applied Mathematics and Mechanics, 2008, 29(9): 1083-1088.
[7]	XIAO Hai-bin. Global Analysis of Ivlev’s Type Predator-Prey Dynamical System[J]. Applied Mathematics and Mechanics, 2007, 28(4): 419-427.
[8]	CAI Ming, LIU Ji-ke, LI Jun. Incremental Harmonic Balance Method for Airfoil Flutter With Multiple Strong Nonlinearities[J]. Applied Mathematics and Mechanics, 2006, 27(7): 833-838.
[9]	LUO Hai-ying, LI Ji-bin. What Are the Separatrix Values Named by Leontovich on Homoclinic Bifurcation[J]. Applied Mathematics and Mechanics, 2005, 26(4): 418-425.
[10]	HE Ze-rong, WANG Mian-se, WANG Feng. Optimal Dynamical Balance Harvesting for a Class of Renewable Resources System[J]. Applied Mathematics and Mechanics, 2004, 25(4): 433-440.
[11]	HUANG Si-xun, XIANG Jie, HAN Wei. Nonlinear Analysis of Equatorial Eastern Pacific Air-Sea Coupling Oscillation and a Limit-Cycle Theory for ENSO Cycle[J]. Applied Mathematics and Mechanics, 2004, 25(5): 472-480.
[12]	HAN Mao-an, GU Sheng-shi. Bifurcations of Subharmonic Solutions in Periodic Perturbation of a Hyperbolic Limit Cycle[J]. Applied Mathematics and Mechanics, 2002, 23(8): 871-875.
[13]	CHENG Chang-jun, ZHANG Neng-hui. Dynamical Behavior of Viscoelastic Cylindrical Shells Under Axial Pressures[J]. Applied Mathematics and Mechanics, 2001, 22(1): 1-8.
[14]	Shen Boqian. An Analogue Rotated Vector Field of Polynomial System[J]. Applied Mathematics and Mechanics, 2000, 21(5): 541-546.
[15]	Cheng Fude. Limit Circles Bifurcated from a Soft Spring Duffing Equation under Perturbation[J]. Applied Mathematics and Mechanics, 1998, 19(2): 121-125.
[16]	Xu Rong-liang, Zhou Guo-cai, Sun Zhao. The Existence of Limit Cycles For The System X=Q(X,y),y=p(X)[J]. Applied Mathematics and Mechanics, 1995, 16(1): 53-59.
[17]	Cheng You-liang, Dai Shi-qiang. Asymptotic Analysis if a Class of Nonlinear Oscillation Equation in Electrical Engineering[J]. Applied Mathematics and Mechanics, 1994, 15(1): 7-12.
[18]	Lin Xiao-lin, Dang Xin-yi. On the(1,3)Distributions of Limit Cycles of Plane Gaudratic Systems[J]. Applied Mathematics and Mechanics, 1994, 15(5): 443-455.
[19]	Yang Hong-chun, Xu Zhen-yuan. Asymptotic Solution of Brusselator Limit Cycle in Biochemistry[J]. Applied Mathematics and Mechanics, 1993, 14(4): 363-366.
[20]	Wang Cheng-wen. A Class of Kolmogorov’s Ecological System with Prey Having Constant Adding Rate[J]. Applied Mathematics and Mechanics, 1992, 13(4): 327-334.