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Original Articles

Stable Attracting Sets in Delay Differential Equations and in Their Runge–Kutta Discretizations

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Pages 791-801 | Published online: 17 Sep 2008

REFERENCES

  • A. Bellen and M. Zennaro ( 2003 ). Numerical Methods for Delay Equations . Oxford University Press , Oxford .
  • O. Diekmann , S.A. van Gils , S.M. Verduyn Lunel , and H.-O. Walther ( 1995 ). Delay Equations: Functional-, Complex-, and Nonlinear Analysis . Springer , Heidelberg .
  • R.D. Driver ( 1977 ). Ordinary and Delay Differential Equations . Applied Mathematical Sciences 20 . Springer , Heidelberg .
  • J. Dugundji ( 1966 ). Topology . Allyn and Bacon , Boston .
  • G. Farkas ( 2001 ). A Hartman-Grobman result for retarded functional differential equations with an application to the numerics around hyperbolic equilibria . ZAMP 52 : 421 – 432 .
  • G. Farkas ( 2003 ). Discretizing hyperbolic periodic orbits of delay equations . ZAMM 83 : 38 – 49 .
  • J.K. Hale ( 1988 ). Asymptotic Behavior of Dissipative Dynamical Systems . American Mathematical Society , Providence , RI .
  • J.K. Hale and S.M. Verduyn Lunel ( 1993 ). Introduction to Functional Differential Equations . Springer , Heidelberg .
  • E. Hairer , S.P. N⊘rsett , and G. Wanner (1993). Solving Ordinary Differential Equations I. , 2nd ed. Springer , Heidelberg.
  • K. In't Hout and C. Lubich ( 1998 ). Periodic orbits of delay differential equations under discretization . BIT Numerical Mathematics 38 : 72 – 91 .
  • P. Kloeden and J. Lorenz ( 1986 ). Stable attracting sets in dynamical systems and in their one-step discretizations . SIAM J. Numer. Anal. 23 : 986 – 993 .
  • T. Yoshizawa ( 1966 ). Stability Theory by Lyapunov's Second Method . The Mathematical Society of Japan , Tokyo .

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