Stability and bifurcation behaviour of genetic regulatory systems with two delays

Comptes Rendus de L'Academie Bulgare des Sciences

Volumn 61, Issue 5, 2008, Pages 585-594

  Nikolov, Svetoslav ^a  

^a INSTITUTE OF MECHANICS   (Bulgaria)

Author keywords

Andronov Hopf bifurcation; Delay differential equations; Stability

Indexed keywords

EID: 47049091445     PISSN: 13101331     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. SMOLEN P., D. A. BAXTER. J. Burne. Am. J. Physiol., 274, 1998, No 2, 532-542.
2. SALASAR C., T. HOFER. BioSystems, 83, 2006, No 2, 195-206.
3. CHEN L., K. AIHARA. IEEE Trans. Circuits Syst., 49, 2002, No 10, 1429-1436.
4. WOLF D., E. EECKMAN. J. Theor. Biol., 195, 1998, No 2, 167-186.
5. ROZEMA D., D. LEWIS. Targets, 2, 2003, 253-259.
6. NIKOLOV S., V. PETROV, V. KOTEV, G. GEORGIEV. In: Handbook of Research on Systems Biology Applications in Medicine, Dauphin County, Idea Group Inc., 2008.
7. JONG H. J. of Comp. Biol., 9, 2002, No 1, 67-103.
8. MARSDEN J., M. MCCRACKEN. The Hopf Bifurcation and its Applications, New York, Springer-Verlag, 1976.
9. BAUTIN N. Behaviour of Dynamical Systems Near the Boundary of Stability, Moscow, Nauka, 1984.
10. BERGSTROM C., E, MCKITTRICK, R. ANTIA. Proc. Natl. Acad. Sci. USA, 100, 2003, 11511-11516.
11. NIKOLOV S., V. PETROV. J. of Mech. in Med. and Biol., 7, 2007, No 3, 297-314.
12. ADIMY M., F. CRAUSTE, SH. RUAN. J. of Theor. Biol., 242, 2006, 288-299.
13. NIKOLOV S., J. VERA, V. KOTEV, O. WOLKENHAUER, V. PETROV. BioSystems, 91, 2008, 51-68.
14. RATEITSCHAK K., O. WOLKENHAUER. Math. Biosci., 205, 2007, 163-179.
15. BELLMAN R., K. COOKE. Differential-Difference Equations. New York, Academic Press, 1963.
16. RUAN SH., J. WEI. Dynamics of Continuous, Discrete and Impulsive Systems. Series A: Math. Analysis, 10, 2003, 863-874.
17. WEI J., SH. RUAN. Physica D, 130, 1999, 255-272.
18. KHAN Q., D. GREENHAGH. IMA J. Math. Appl. Med. Biol., 16, 1999, 133-142.