Efficient and reliable stability analysis of solutions of delay differential equations

Nonlinear Science and Complexity-Proceedings of the Conference: Volume 1

Volumn , Issue , 2006, Pages 109-120

  Verheyden, Koen ^a   Luzyanina, Tatyana ^b   Roose, Dirk ^a  

^a Department of Computer Science KU Leuven   (Belgium)

^b INSTITUTE OF MATHEMATICAL PROBLEMS OF BIOLOGY   (Russian Federation)

Author keywords

Characteristic roots; Delay differential equations; Stability analysis

Indexed keywords

EID: 84892353714     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812772428_0013     Document Type: Chapter

References (12)

1. D. BREDA, Solution operator approximation for delay differential equation characteristic roots computation via Runge-Kutta methods, Appl. Numer. Math, to appear.
2. D. BREDA, S. MASET, AND R. VERMIGLIO, Computing the characteristic roots for delay differential equations, IMA J. Numer. Anal., 24 (2004), pp. 1-19.
3. D. BREDA, S. MASET, AND R. VERMIGLIO, Pseudospectral differencing methods for characteristic roots of delay differential equations, SIAM J. Sci. Comput., 27 (2005), pp. 482-495.
4. K. ENGELBORGHS, T. LUZYANINA, AND D. ROOSE, Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL, ACM Trans. Math. Softw., 28 (2002), pp. 1-21.
5. K. ENGELBORGHS, T. LUZYANINA, AND G. SAMAEY, DDE-BIFTOOL v. 2.00: a Matlab package for numerical bifurcation analysis of delay differential equations, Report TW 330, Department of Computer Science, K.U.Leuven, Leuven, Belgium, 2001. Available from http://www.cs.kuleuven.be/~twr/research/software/delay/ddebiftool.shtml
6. K. ENGELBORGHS AND D. ROOSE, On stability of LMS methods and characteristic roots of delay differential equations, SIAM J. Numer. Anal., 40 (2002), pp. 629-650.
7. E. HAIRER AND G. WANNER, Solving ordinary differential equations. II: Stiff and differentialalgebraic problems, vol. 14 of Springer series in computational mathematics, Springer Berlin, 2nd ed., 1996.
8. J. HALE AND S. M. VERDUYN LUNEL, Introduction to Functional Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer-Verlag, 1993.
9. K. VERHEYDEN, K. GREEN, AND D. ROOSE, Numerical stability analysis of a large-scale delay system modelling a lateral semiconductor laser subject to optical feedback, Phys. Rev. E 69, 036702 (2004).
10. K. VERHEYDEN, T. LUZYANINA, AND D. ROOSE, Location and numerical preservation of characteristic roots of delay differential equations by LMS methods., Technical Report TW-382, Department of Computer Science, K.U.Leuven, Leuven, Belgium, Dec. 2003. Available from http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW382.abs.html
11. K. VERHEYDEN AND D. ROOSE, Efficient numerical stability analysis of delay equations: a spectral method, in the Proceedings of the IFAC Workshop on Time-Delay Systems 2004, D. Roose and W. Michiels, eds., IFAC Proceedings Volumes, 2004, pp. 209-214.
12. K. VERHEYDEN, T. LUZYANINA, AND D. ROOSE, Efficient computation of characteristic roots of delay differential equations using LMS methods., submitted. Available from http://www.cs.kuleuven.be/~koenv/preprints.html