Ultimate stability of a type of characteristic equation with delay dependent parameters

Journal of Systems Science and Complexity

Volumn 19, Issue 1, 2006, Pages 137-144

  Li, Jianquan ^a,b   Ma, Zhien ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b AIR FORCE ENGINEERING UNIVERSITY   (China)

Author keywords

Characteristic equation; Time delay; Ultimate stability

Indexed keywords

EID: 33748942134     PISSN: 10096124     EISSN: 15597067     Source Type: Journal    
DOI: 10.1007/s11424-006-0137-x     Document Type: Article

References (10)

1. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993.
2. K. L. Cooke and Z. Grossman, Discrete delay, distributed delay and stability switches, J. math. Anal. Appl., 1982, 86: 592-627.
3. K. L. Cooke and P. van den Driessche, On zeros of some transcendental equation, Funkcial. Evac., 1986, 29: 77-90.
4. Qing Huang and Zhien Ma, On stability of some transcendental equation, Ann. of Diff. Eqs., 1990, 6: 21-31.
5. W. G. Aiello, H. I. Freedman and J. Wu, A model of stage structured population growth with density dependent time delay, SIAM J. Apl. Math., 1992, 52: 855-569.
6. J. Li and Z. Ma, Global analysis of SIS epidemic models with variable table population size, Mathematical and Computer Modelling, 2004, 39: 1231-1242.
7. K. L. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol., 1999, 39: 332-352.
8. K. L. Cooke and P. van den Driessche, Analysis of an SEIS epidemic model with two delays, J. Math. Biol., 1996, 35: 240-260.
9. E. Beretta, and Y. Kuang, Geometric stability switch criteria, in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 2002, 33: 1144-1165.
10. J. Li and Z. Ma, Stability switches in a class of characteristic equations with delay-dependent parameters, Nonlinear Analysis: Real World Applications, 2004, 5: 389-408.