Complex dynamics in delay-differential equations with large delay

European Physical Journal: Special Topics

Volumn 191, Issue 1, 2011, Pages 91-103

  Wolfrum, M ^a   Yanchuk, S ^b   Hovel P ^c   Scholl E ^c  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b HUMBOLDT UNIVERSITY   (Germany)

^c TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79952011513     PISSN: 19516355     EISSN: 19516401     Source Type: Journal    
DOI: 10.1140/epjst/e2010-01343-7     Document Type: Review

References (43)

1. T. Erneux, Applied delay differential equations (Springer, 2009).
2. F. M. Atay (Ed.), Complex Time-Delay Systems (Springer, Berlin Heidelberg, 2010).
3. W. Just, A. Pelster, M. Schanz, E. Schöll (eds.), Delayed Complex Systems, Theme Issue of Phil. Trans. R. Soc. A 368, 301 (2010).
4. P. Hövel, Control of Complex Nonlinear Systems with Delay (Springer, Heidelberg, 2010).
5. K. Pyragas, Phys. Lett. A 170, 421 (1992).
6. E. Schöll, H. G. Schuster (Eds.), Handbook of Chaos Control (Wiley-VCH, Weinheim, 2008),second completely revised and enlarged edition.
7. M. G. Rosenblum, A. S. Pikovsky, Phys. Rev. Lett. 92, 114102 (2004).
8. A. Ahlborn, U. Parlitz, Phys. Rev. E 72, 016206 (2005).
9. P. Hövel, E. Schöll, Phys. Rev. E 72, 046203 (2005).
10. T. Dahms, P. Hövel, E. Schöll, Phys. Rev. E 76, 056201 (2007).
11. A. Gjurchinovski, V. Urumov, Europhys. Lett. 84, 40013 (2008).
12. A. Gjurchinovski, V. Urumov, Phys. Rev. E 81, 16209 (2010).
13. S. Bielawski, M. Bouazaoui, D. Derozier, P. Glorieux, Phys. Rev. A 47, 3276 (1993).
14. A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, D. J. Gauthier, Chaos 8, 782 (1998).
15. K. Pyragas, V. Pyragas, I. Z. Kiss, J. L. Hudson, Phys. Rev. Lett. 89, 244103 (2002).
16. K. Pyragas, V. Pyragas, I. Z. Kiss, J. L. Hudson, Phys. Rev. E 70, 026215 (2004).
17. K. B. Blyuss, Y. N. Kyrychko, P. Hövel, E. Schöll, Eur. Phys. J. B 65, 571 (2008).
18. Y. N. Kyrychko, K. B. Blyuss, P. Hövel, E. Schöll, Dyn. Sys. 24, 361 (2009).
19. A. Ahlborn, U. Parlitz, Phys. Rev. Lett. 93, 264101 (2004).
20. E. Schöll, in Nonlinear Dynamics of Nanosystems, edited by G. Radons, B. Rumpf, H. G. Schuster (Wiley-VCH, Weinheim, 2009), ISBN 978-3-527-40791-0.
21. L. Schimansky-Geier, B. Fiedler, J. Kurths, E. Schöll (Eds.), Analysis and control of complex nonlinear processes in physics,chemistry and biology (World Scientific,Singapore, 2007).
22. S. Schikora, P. Hövel, H. J. Wünsche, E. Schöll, F. Henneberger, Phys. Rev. Lett. 97, 213902 (2006).
23. R. Lang, K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
24. J. Mørk, B. Tromborg, J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
25. A. M. Levine, G. H. M. van Tartwijk, D. Lenstra, T. Erneux, Phys. Rev. A 52, R3436 (1995).
26. P. M. Alsing, V. Kovanis, A. Gavrielides, T. Erneux, Phys. Rev. A 53, 4429 (1996).
27. T. Dahms, P. Hövel, E. Schöll, Phys. Rev. E 78, 056213 (2008).
28. J. E. S. Socolar, D. W. Sukow, D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
29. M. Wolfrum, S. Yanchuk, Phys. Rev. Lett. 96, 220201 (2006).
30. S. Yanchuk, M. Wolfrum, P. Hövel, E. Schöll, Phys. Rev. E 74, 026201 (2006).
31. S. Yanchuk, M. Wolfrum, SIAM J. Appl. Dynam. Syst. 9, 519 (2010).
32. M. Lichtner, M. Wolfrum, S. Yanchuk, Preprint 647, DFG Research Center Matheon, Berlin (2009).
33. S. Yanchuk, P. Perlikowski, Phys. Rev. E 79, 046221 (2009).
34. M. Nizette, Phys. Rev. E 70, 056204 (2004).
35. S. A. Kashchenko, Siberian Math. J. 40, 483 (1999).
36. G. Giacomelli, A. Politi, Phys. Rev. Lett. 76, 2686 (1996).
37. L. S. Tuckerman, D. Barkley, Physica D 46, 57 (1990).
38. J. Mulet, C. R. Mirasso, Phys. Rev. E 59, 5400 (1999).
39. M. Wolfrum, D. Turaev, Opt. Comm. 212, 127 (2002).
40. M. Peil, T. Heil, I. Fischer, W. Elsäßer, Phys. Rev. Lett. 88, 174101 (2002).
41. V. Z. Tronciu, H.-J. Wünsche, M. Wolfrum, M. Radziunas, Phys. Rev. E 73, 046205 (2006).
42. A. Ritter, H. Haug, J. Opt. Soc. Am. B 10, 130 (1993).
43. A. Ritter, H. Haug, J. Opt. Soc. Am. B 10, 145 (1993).