On global properties of time-delayed feedback control: Weakly nonlinear analysis

Physica D: Nonlinear Phenomena

Volumn 199, Issue 1-2, 2004, Pages 33-44

  Just, Wolfram ^a   Benner, Hartmut ^b   Von Loewenich, Clemens ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Codimension two bifurcations; Control of chaos; Differential difference equations; Hysteresis

Indexed keywords

CHAOS THEORY; COMPUTER SIMULATION; DIFFERENCE EQUATIONS; FERROMAGNETIC RESONANCE; HYDRODYNAMICS; HYSTERESIS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PARAMETER ESTIMATION;

CODIMENSION TWO BIFURCATIONS; CONTROL OF CHAOS; DIFFERENTIAL-DIFFERENCE EQUATIONS; DYNAMICS SYSTEMS;

FEEDBACK CONTROL;

EID: 9644254157     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2004.08.002     Document Type: Conference Paper

References (24)

1. E. Ott, C. Grebogi, Y.A. Yorke, Controlling Chaos, Phys. Rev. Lett. 64 (1990) 1196.
2. R. Bellmann, Dynamic Programming and Modern Control Theory, Academic Press, New York, 1965.
3. H. Nijmeijer, A. Schaft, Nonlinear Dynamical Control Systems, Springer-Verlag, New York, 1996.
4. K. Ogata, Modern Control Engineering, Prentice-Hall, New York, 1997.
5. T. Shinbrot, Progress in the control of chaos, Adv. Phys. 44 (1995) 73.
6. K. Pyragas, Continuous control of chaos by self-controlling feedback, Phys. Lett. A 170 (1992) 421.
7. 0. Lüthje, S. Wolff, G. Pfister, Control of chaotic Taylor-Couette flow with time-delayed feedback, Phys. Rev. Lett. 86 (2001) 1745.
8. S. Bielawski, D. Derozier, P. Glorieux, Experimental characterization of unstable periodic orbits by controlling chaos, Phys. Rev. A 47 (1993) R2492.
9. H. Benner, W. Just, Control of chaos by time delayed feedback in high power ferromagnetic resonance experiments, J. Kor. Phys. Soc. 40 (2002) 1046.
10. P. Parmananda, R. Madrigal, M. Rivera, L. Nyikos, I.Z. Kiss, V. Gáspár, Stabilization of unstable steady states and periodic orbits in an electrochemical system using delayed-feedback control, Phys. Rev. E 59 (1999) 5266.
11. J.K. Hale, S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
12. M.E. Bleich, J.E.S. Socolar, Controlling spatiotemporal dynamics with time-delayed feedback, Phys. Rev. E 54 (1996) R17.
13. H. Nakajima, On analytical properties of delayed feedback control of chaos, Phys. Lett. A 232 (1997) 207.
14. W. Just, T. Bernard, M. Ostheimer, E. Reibold, H. Benner, Mechanism of time-delayed feedback control, Phys. Rev. Lett. 78 (1997) 203.
15. H.G. Schuster (Ed.), Handbook of Chaos Control, Wiley-VCH, Berlin, 1999.
16. Y.-C. Lai, C. Grebogi, J.A. Yorke, S.C. Venkataramani, Riddling bifurcation in chaotic dynamical systems, Phys. Rev. Lett. 77 (1996) 55.
17. B. Krauskopf, K. Green, Computing unstable manifolds of periodic orbits in delay differential equations, J. Comp. Phys. 186 (2003) 230.
18. W. Just, E. Reibold, H. Benner, K. Kacperski, F. Fronczak, J. Hołyst, Limits of time-delayed feedback control, Phys. Lett. A 254 (1999) 158.
19. W. Just, H. Benner, E. Reibold, Theoretical and experimental aspects of chaos control by time-delayed feedback, Chaos 13 (2003) 259.
20. J.E.S. Socolar, D.W. Sukow, D.J. Gauthier, Stabilizing unstable periodic orbits in fast dynamical systems, Phys. Rev. E 50 (1994) 3245.
21. O. Beck, A. Amann, E. Schöll, J.E.S. Socolar, W. Just, Comparison of time-delayed feedback schemes for spatio-temporal control of chaos in a reaction-diffusion system with global coupling, Phys. Rev. E 66 (2002) 016213.
22. F. Giannakopulos, A. Zapp, Bifurcations in a planar system of differential delay equations modeling neural activity, Physica D 159 (2001) 215.
23. B.F. Redmond, V.G. LeBlanc, A. Longtin, Bifurcation analysis of a class of first-order nonlinear delay-differential equations with reflectional symmetry, Physica D 166 (2002) 131.
24. M. Schanz, A. Pelster, Analytical and numerical investigations of the phase-locked loop with time delay, Phys. Rev. E 67 (2003) 056205.