Qualitative analysis for the merkin enzyme reaction system

Journal of Biological Systems

Volumn 10, Issue 2, 2002, Pages 167-182

  Wang, Yuquan ^b   Shen, Zuorui ^a  

^a CHINA AGRICULTURAL UNIVERSITY   (China)

^b NANJING AGRICULTURAL UNIVERSITY   (China)

Author keywords

Enzyme reaction system; Global stability; Hopf bifurcations; Limit cycles

Indexed keywords

EID: 0347303197     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339002000500     Document Type: Article

References (12)

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3. Gray P., Instabilities and oscillations in chemical reactions in closed and open systems, Proc. R. Soc. Lond. A 415 (1988) pp. 1-34.
4. Hassard B. D., Kazarinoff N. D. and Wan Y. H., Theory and Application of Hopf Bifurcation (Cambridge University Press, Cambridge, 1981).
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7. Merkin J. H., Needham D. J. and Scott S. K., A simple model for sustained oscillations in isothermal branched-chain or autocatalytic reactions in a well stirred open system, II. Limit cycles and non-stationary states, Proc. R. Soc. Lond. A 398 (1985) pp. 101-116.
8. Merkin J. H., Needham D. J. and Scott S. K., Oscillatory chemical reactions in closed vessels, Proc. R. Soc. Lond. A 406 (1986) pp. 299-323.
9. Metcalf M. J., Merkin J. H. and Scott S. K., Reaction-diffusion waves in coupled isothermal autocatalytic chemical systems, IMA Journal of Applied Mathematics 51 (1993) pp. 269-298
10. Metcalf M. J., Merkin J. H. and Scott S. K., Oscillating wave fronts in isothermal chemical systems with arbitrary powers of autocatalysis, Proc. R. Soc. Lond. A 447 (1994) pp. 155-174.
11. Needham D. J., King A. C. and Merkin J. H., A reaction-diffusion model for autocatalytic polymerization: I. Permanent form travelling waves, IMA Journal of Applied Mathematics 53 (1994) pp. 137-149.
12. Needham D. J., King A. C. and Merkin J. H., A reaction-diffusion model for autocatalytic polymerization: II. The initial value problem, IMA Journal of Applied Mathematics 56 (1996) pp. 65-86.