Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

HOPF BIFURCATION IN NUMERICAL APPROXIMATION FOR DELAY DIFFERENTIAL EQUATIONS

  • Zhang, Chunrui (Key Laboratory of Forestry Plant Ecology, Ministry of Education, Northeast Forestry University) ;
  • Liu, Mingzhu (Department of Mathematics, Harbin Institute of Technology) ;
  • Zheng, Baodong (Department of Mathematics, Harbin Institute of Technology)
  • Published : 2004.01.01

⟨ Previous Next ⟩

Abstract

In this paper we investigate the qualitative behaviour of numerical approximation to a class delay differential equation. We consider the numerical solution of the delay differential equations undergoing a Hopf bifurcation. We prove the numerical approximation of delay differential equation had a Hopf bifurcation point if the true solution does.

Keywords

References

  1. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields J. Guckenheimer;P. J. Holmes
  2. Introduction to applied nonlinear dynamical systems and chaos S. Wiggins
  3. Theory and Applications of Hopf Bifurcation B. D. Hassard;N. D. Kazarinoff;Y. H. Wan
  4. Introduction to Functional Differential Equations J. K. Hale;S. M. Verdyn Lunel
  5. JCAM v.115 Numerical hopf bifurcation for a class of delay differential equations Neville J. Ford;Volker Wulf
  6. JCAM v.111 The use of boundary locus plots in the identification of bifurcation point in numerical approximation of delay differential equations Neville J. Ford;Volker Wulf
  7. Technical Report 323, Manchester Center for Computational Mathematics Numerical hopf bifurcation for the delay logistic equation Neville J. Ford;Volker Wulf
  8. BIT v.39 Naimark-Sacker bifurcations in the Euler method for a delay differential equations T. Koto