Control of time-delayed feedback systems with application to optics†

REFERENCES

• CELKA , P. , 1994 , Experimental verification of Pyragas's chaos control method applied to Chua's circuit . International Journal of Bifurcations and Chaos , 4 , 1703 – 1706 .
   Google Scholar
• CHEN , G. , and DONG , X. , 1993a , From chaos to order—perspectives and methodologies in controlling chaotic nonlinear dynamical systems . International Journal of Bifurcation and Chaos , 3 , 1363 – 1409 ; |ot1193 b, On feedback control of chaotic continuous-time systems. IEEE Transaction on Circuits and Systems, 40, 591–601.
   Web of Science ®Google Scholar
• DEDIEU , H. , and OGORZALEK , M. J. , 1993 , Controlling chaos in Chua's circuit via sampled inputs . International Journal of Bifurcations and Chaos , 4 , 447 – 455 .
   Google Scholar
• DITTO , W. L. , RAUSEO , S. N. , and SPANO , M. I. , 1990 , Experimental control of chaos . Physical Review Letters , 65 , 3211 – 3214 .
   PubMed Web of Science ®Google Scholar
• HEIDEN, U. AN DER and WALTER , H.-O. , 1983 , Existence of chaos in control system with delayed feedback . Journal of Differential Equations , 47 , 273 – 295 .
   Google Scholar
• HOPE , F. A. , KAPLAN , D. L. , GIBBS , H. M. , and SHOEMAKER , R. L. , 1982 , Bifurcations to chaos in optical bistability, Physical Review A , 25 , 2172 – 2182 .
   Google Scholar
• IKEDA , K. , KONDO , K. , and AKIMOTO , O. , 1982 , Successive higher-harmonic bifurcations in systems with delayed feedback . Physical Review Letters , 49 , 1467 – 1470 .
   Google Scholar
• IKKDA , K. , and MATSUMOTO , K. , 1987 , High-dimensional chaotic behaviour in systems with time-delayed feedback . Physica D , 29 , 223 – 235 .
   Google Scholar
• JOHNSON , G. A. , and HUNT , E. R. , 1993 , Controlling chaos in a simple autonomous system Chua's circuit . International Journal of Bifurcations and Chaos , 3 , 789 – 792 .
   Google Scholar
• KAPITANIAK , T. , CHUA, L, O., and ZIIONG , G.-Q. , 1994 , Experimental synchronization of chaos using continuous control . International Journal of Bifurcations and Chaos , 4 , 483 – 488 .
   Google Scholar
• LI-PRI , S. , GIACOMELLI , G. , POLITI , A. , and ARECCHI , F. T. , 1993 , High-dimensional chaos in delayed dynamical systems . Physica D , 70 , 235 – 249 .
   Google Scholar
• OGORZALEK , M. J. , 1993 , Taming chaos Part U-Control . IEEE Transaction on Circuits and Systems I , 40 , 700 – 706 .
   Google Scholar
• OTT , E. , GREBOGI, C, and YORKE , J. A. , 1990 , Controlling chaos . Physical Review Letters , 64 , 1196 – 1199 .
   PubMed Web of Science ®Google Scholar
• PYRAGAS , K. , 1992 , Continuous control of chaos by self-controlling systems . Physics Letters , A 170 , 421 – 428 .
   Google Scholar
• PYRAGAS , K. , and TAMASEVICIUS , A. , 1993 , Experimental control of chaos by delayed self-controlling feedback . Physics Letters , A 180 , 99 – 102 .
   Google Scholar
• SCHOLL, E.. and PYRAGAS , K. , 1993 , Tunable semiconductor oscillator based on self-control of chaos in the dynamic hall effect . Europhysics Letters , 24 , 159 – 164 .
   Google Scholar
• †A shorter form of this paper was presented at the 1994 Workshop on the Nonlinear Dynamics of Electronic Systems (NDES'94) held at the University of Mining and Metallurgy, Krakow, Poland, on 29-30 July.
   Google Scholar