Dynamics of a nonstandard finite-difference scheme for Mackey-Glass system

Journal of Mathematical Analysis and Applications

Volumn 344, Issue 2, 2008, Pages 932-941

  Su, Huan ^a   Ding, Xiaohua ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Hopf bifurcation; Mackey Glass system; Nonstandard finite difference; Stability

Indexed keywords

EID: 43449118048     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.03.044     Document Type: Article

References (11)

1. Mackey M.C., and Glass L. Oscillations and chaos in physiological control systems. Science 197 (1977) 287-289
2. Wulf V., and Ford N.J. Numerical Hopf bifurcation for a class of delay differential equation. J. Comput. Appl. Math. 115 (2000) 601-616
3. Hassard B.D., Kazarinoff N.D., and Wa Y.H. Theory and Applications of Hopf Bifurcation (1981), Cambridge University Press, Cambridge
4. Stuart A.M., and Humphries A.R. Dynamical Systems and Numerical Analysis (1998), Cambridge University
5. Yuri A.K. Elements of Applied Bifurcation Theory (1995), Springer-Verlag, New York
6. Mickens R.E. A nonstandard finite-difference scheme for the Lotka-Volterra system. Appl. Numer. Math. 45 (2003) 309-314
7. Patidar K.C. On the use of nonstandard finite difference methods. J. Difference Equ. Appl. 11 8 (2005) 735-758
8. Dieudonne J. Foundations of Modern Analysis (1960), Academic Press, New York
9. Wulf V. Numerical Analysis of Delay Differential Equations Undergoing a Hopf Bifurcation (1999), University of Liverpool
10. Wiggins S. Introduction to Applied Nonlinear Dynamical System and Chaos (1990), Springer-Verlag, New York
11. Ruan S., and Wei J. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 10 (2003) 863-874