Abstract
We review the subject of control of chaotic systems paying special attention to exponential control. We also discuss the application of synchronization of chaotic systems to security in communications.
Similar content being viewed by others
References
E Ott, C Grebogi and J A Yorke,Phys. Rev. Lett. 64, 1196 (1990)
F Takens, inDynamical systems and turbulence, edited by D Rand and L S Young (Springer-Verlag, Berlin, 1981)
G H Gunaratne, P S Linsay and M J Vinson,Phys. Rev. Lett. 63, 1 (1989)
W L Ditto, S N Rauseo and M L Spano,Phys. Rev. Lett. 65, 3211 (1990)
A Azevedo and S M Rezende,Phys. Rev. Lett. 66, 1342 (1991)
B Peng, V Petrov and K Showalter,J. Phys. Chem. 95, 4957 (1991)
E R Hunt,Phys. Rev. Lett. 67, 1953 (1991)
R Roy, T W Murphy Jr, T D Maier, Z Gills and E R Hunt,Phys. Rev. Lett. 68, 1259 (1992)
C Reyl, L Flepp, R Badii and E Brun,Phys. Rev. E47, 267 (1993)
A Garfinkel, W L Ditto, M L Spano and J Weiss,Science 257, 1230 (1992)
T Shinbrot, E Ott, C Grebogi and J A Yorke,Phys. Rev. Lett. 65, 3215 (1990);Phys. Rev. A45, 4165 (1992)
T Shinbrot, W Ditto, C Grebogi, E Ott, M Spano and J A Yorke,Phys. Rev. Lett. 68, 2863 (1992)
B A Huberman and E Lumer,IEEE Trans. Circuit Syst. 37, 547 (1990)
U Dressler and G Nitsche,Phys. Rev. Lett. 68, 1 (1992)
R W Rollins, P Parmananda and P Sherad,Phys. Rev. E47, R780 (1993)
Y C Lai, M Ding and C Grebogi,Phys. Rev. E47, 86 (1993)
Y C Lai, M Ding and C Grebogi,Phys. Rev. E49, 1094 (1994)
J Alvarez-Ramírez,Phys. Rev. E48, 3165 (1994)
T C Newell, P N Alsing, A Gavrielides and V Koranis,Phys. Rev. E49, 313 (1994)
S Bielawski, D Derozier and P Gloreieux,Phys. Rev. E49, R971 (1994)
K Pyragas,Phys. Lett. A170, 421 (1992)
Z Qu, G Hu and B Ma,Phys. Lett. A178, 265 (1993)
K Pyragas,Phys. Lett. A181, 203 (1993)
A Kittle, K Pyragas and R Richtor,Phys. Rev. E50, 262 (1994)
M A Matias and J Güémez,Phys. Lett. A181, 29 (1993)
M A Matias and J Güémez,Phys. Rev. Lett. 72, 1455 (1994)
B Peng, S K Scott and K Showalter,J. Phys. Chem. 94, 1134 (1991)
J Singer, Y Z Wang and H H Bau,Phys. Rev. Lett. 66, 1123 (1993)
Y H Chen and M Y Chou,Phys. Rev. E50, 2331 (1994)
S Sinha, R Ramaswamy and J S Rao,Physica D43, 118 (1990)
J K John and R E Amritkar,Phys. Rev. E49, 4843 (1994)
E A Jackson,Phys. Rev. A44, 4839 (1991)
R Lima and M Pettini,Phys. Rev. A41, 726 (1990)
Y Braiman and I Goldhirsh,Phys. Rev. Lett. 66, 2545 (1991)
G Chen and X Dong,Int. J. Bifur. Chaos 2, 407 (1992)
S Rajasekar and M Lakshmanan,Physica D67, 282 (1993)
S Rajasekar,Chaos, Solitons and Fractals 5, 2135 (1995)
S Parthasarthy and S Sinha,Phys. Rev. E51, 6239 (1995)
K Chakrabarty and S Banerjee,Phys. Lett. A200, 115 (1995)
L M Pecora and T L Carroll,Phys. Rev. Lett. 64, 821 (1990);Phys. Rev. A44, 2374 (1991)
T L Carroll and L M Pecora,IEEE Trans. Circuits Syst. 38, 453 (1991);40, R1620 (1993)
R E Amritkar and N Gupte,Phys. Rev. A49, R3403 (1991)
L M Pecora and T L Carroll,Phys. Rev. Lett. 67, 945 (1991);Phys. Rev. E48, 2426 (1993)
T Kapitaniak,Phys. Rev. E50, 1642 (1994)
K Murali and M Lakshmanan,Phys. Rev. E49, 4882 (1994)
M Ding and E Ott,Phys. Rev. E149, R495 (1994)
K M Cuomo and A V Oppenheim,Phys. Rev. Lett. 71, 65 (1993)
N Gupte and R E Amritkar,Phys. Rev. E48, R1620 (1993)
S D Gadre and V S Varma,Pramana — J. Phys. 43, 431 (1994)
S D Gadre and V S Varma,Pramana — J. Phys. 45, 355 (1995)
E N Lorenz,J. Atoms. Sci. 20, 130 (1976)
M Hénon,Commun. Math. Phys. 50, 69 (1976)
C Sparrow,The Lorenz equations, bifurcations and chaos (Springer Verlag, New York, 1982)
T Bohr and O B Christensen,Phys. Rev. Lett. 63, 2161 (1989)
K Kaneko,Prog. Theor. Phys. 74, 1033 (1985);Physica (Amsterdam)D23, 437 (1986);D34, 1 (1989);D37, 60 (1989)
J P Crutchfield and K Kaneko, inDirections in chaos edited by Hao Bai-Lin (World Scientific, Singapore, 1987);Phys. Rev. Lett. 60, 2715 (1988)
J D Keeler and J D Farmer,Physica (Amsterdam)D23, 413 (1986)
E J Ding and Y N Lu,J. Phys. A25, 2897 (1992)
G Hu and Z Qu,Phys. Rev. Lett. 72, 68 (1994)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gadre, S.D., Varma, V.S. Control of chaos. Pramana - J Phys 48, 259–270 (1997). https://doi.org/10.1007/BF02845634
Issue Date:
DOI: https://doi.org/10.1007/BF02845634