Local Hopf bifurcation and global existence of periodic solutions in a kind of physiological system

Nonlinear Analysis: Real World Applications

Volumn 8, Issue 5, 2007, Pages 1459-1471

  Ding, Xiaohua ^a   Li, Wenxue ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Global periodic solution; Hopf bifurcation; Physiological control system; Stability

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; NEURAL NETWORKS; PHYSIOLOGICAL MODELS;

GLOBAL PERIODIC SOLUTION; PERIODIC SOLUTIONS; PHYSIOLOGICAL CONTROL SYSTEM; SYMMETRIC FUNCTIONAL DIFFERENTIAL EQUATIONS;

BIFURCATION (MATHEMATICS);

EID: 34547111561     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2006.07.013     Document Type: Article

References (16)

1. Dieudonné J. Foundations of Modern Analysis (1960), Academic Press, New York
2. Glass L., and Mackey M.C. Physiological conditions resulting from instabilities in physiological control system. Ann. New York Acad. Sci. 316 (1979) 214-235
3. Gopalsamy K., Kulenovic M.R.S., and Ladas G. Oscillations and global attractivity in respiratory dynamics. Dyn. Stability System 4 2 (1989) 131-139
4. Gyori I., and Ladas G. Oscillation Theory of Delay Differential Equations with Applications (1991), Academic Press, New York
5. Hale J. Theory of Functional Differential Equations (1977), Springer, New York
6. Hassard B.D., Kazarinoff N.D., and Wan Y.H. Theory and Application of Hopf Bifurcation (1981), Cambridge University Press, Cambridge
7. Mackey M.C., and Glass L. Oscillation and chaos in physiological control system. Science 197 (1977) 287-289
8. Ruan S., and Wei J. Periodic solutions of planar systems with two delays. Proc. R. Soc. Edinburgh A 129 (1999) 1017-1032
9. Ruan S., and Wei J. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dyn. Continuous, Discrete Impulsive Syst. Ser. A: Math. Anal. 10 (2003) 863-874
10. Song Y., and Wei J. Local Hopf bifurcation and global existence of periodic solutions in a delayed predator-prey system. J. Math. Anal. Appl. 301 (2005) 1-21
11. Song Y., Wei J., and Han M. Local and global Hopf bifurcation in a delayed hematopoliesis model. Int. J. Bifurcation Chaos 14 11 (2004) 3909-3919
12. Wei J., and Li M.Y. Hopf bifurcation analysis in a delayed Nicholson blowflies equation. Nonlinear Anal. 60 (2005) 1351-1367
13. Wei J., and Yuan Y. Synchronized Hopf bifurcation analysis in a neural network model with delays. J. Math. Anal. Appl. 312 (2005) 205-229
14. Wei J., and Zou X. Bifurcation analysis of a population model and the resulting SIS epidemic model with delay. J. Comput. Appl. Math. 197 (2006) 169-187
15. Wen X., and Wang Z. The existence of periodic solutions for some model with delay. Nonlinear Anal. Real World Appl. 3 (2002) 567-581
16. Wu J. Symmetric functional differential equations and neural networks with memory. Trans. Amer. Math. Soc. 350 (1998) 4799-4838