The finite-time synchronization for the high-dimensional chaotic system is studied. A method is derived from the finite-time stability theory and adaptive control technique. To show the wider applicability of our method, an illustration is given using four-dimensional (4D) hyperchaotic systems. Numerical simulations are also used to verify the effectiveness of the technique. Then, the synchronization is applied to secure communication through chaos masking. Simulation results show that the two high-dimensional chaotic systems can realize monotonous synchronization, and the information signal, which is masked, can be recovered undistortedly.

References

References
1.
Ott
,
E.
,
Grebogi
,
C.
, and
Yorke
,
J.
,
1990
, “
Controlling Chaos
,”
Phys. Rev. Lett.
,
64
(
11
), pp.
1196
1199
.
2.
Chen
,
D.
,
Zhao
,
W.
,
Sprott
,
J.
, and
Ma
,
X.
,
2013
, “
Application of Takagi-Sugeno fuzzy Model to a Class of Chaotic Synchronization and Anti-Synchronization
,”
Nonlinear Dyn.
,
73
(
3
), pp.
1495
1505
.
3.
Chen
,
D.
,
Zhao
,
W.
,
Ma
,
X.
, and
Wang
,
J.
,
2013
, “
Control for a Class of 4D Chaotic Systems With Random-Varying Parameters and Noise Disturbance
,”
J. Vib. Control
,
19
(
7
), pp.
1080
1086
.
4.
Gan
,
Q.
,
Zhang
,
H.
, and
Dong
,
J.
,
2013
, “
Exponential Synchronization for Reaction-Diffusion Neural Networks With Mixed Time-Varying Delays Via Periodically Intermittent Control
,”
Nonlinear Anal. Modell. Control
,
19
, pp.
1
25
.
5.
Yu
,
X.
, and
Liu
,
G.
,
2014
, “
Output Feedback Control of Nonlinear Systems With Uncertain ISS/iISS Supply Rates and Noises
,”
Nonlinear Anal. Modell. Control
,
19
, pp.
286
299
.
6.
Wang
,
H.
,
Han
,
Z.
,
Xie
,
Q.
, and
Zhang
,
W.
,
2009
, “
Finite-Time Synchronization of Uncertain Unified Chaotic Systems Based on CLF
,”
Nonlinear Anal. RWA
,
10
(
5
), pp.
2842
2849
.
7.
Bhat
,
S.
, and
Bernstein
,
D.
,
1997
, “
Finite-Time Stability of Homogeneous Systems
,” ACC, Albuquerque, NM, pp.
2513
2514
.
8.
Haimo
,
V. T.
,
1986
, “
Finite Time Controllers
,”
SIAM J. Control Optim.
,
24
(
4
), pp.
760
770
.
9.
Sugawara
,
T.
,
Tachikawa
,
M.
,
Tsukamoto
,
T.
, and
Shimizu
,
T.
,
1994
, “
Observation of Synchronization in Laser Chaos
,”
Phys. Rev. Lett.
,
72
(
22
), pp.
3502
3505
.
10.
Artstein
,
Z.
,
1983
, “
Stabilization With Relaxed Controls
,”
Nonlinear Anal. TMA
,
7
(
11
), pp.
1163
1173
.
11.
Yu
,
W.
,
2010
, “
Finite-Time Stabilization of Three-Dimensional Chaotic Systems Based on CLF
,”
Phys. Lett. A
,
374
(
30
), pp.
3021
3024
.
12.
Liu
,
Y.
,
2012
, “
Circuit Implementation and Finite-Time Synchronization of the 4D Rabinovich Hyperchaotic System
,”
Nonlinear Dyn.
,
67
(
1
), pp.
89
96
.
13.
Rössler
,
O. E.
,
1976
, “
An Equation for Continuous Chaos
,”
Phys. Lett. A
,
57
(
5
), pp.
397
398
.
14.
Buscarino
,
A.
,
Fortuna
,
L.
, and
Frasca
,
M.
,
2009
, “
Experimental Robust Synchronization of Hyperchaotic Circuits
,”
Physica D
,
238
(
18
), pp.
1917
1922
.
15.
Yang
,
X.
, and
Cao
,
J.
,
2010
, “
Finite-Time Stochastic Synchronization of Complex Networks
,”
Appl. Math. Modell.
,
34
(
11
), pp.
3631
3641
.
16.
Yang
,
X.
,
Cao
,
J.
, and
Lu
,
J.
,
2011
, “
Synchronization of Delayed Complex Dynamical Networks With Impulsive and Stochastic Effects
,”
Nonlinear Anal. RWA
,
12
(
4
), pp.
2252
2266
.
17.
Shen
,
J.
, and
Cao
,
J.
,
2011
, “
Finite-Time Synchronization of Coupled Neural Networks Via Discontinuous Controllers
,”
Cognit. Neurodyn.
,
5
(
4
), pp.
373
385
.
18.
Chen
,
D.
,
Lin
,
S.
,
Chen
,
H.
, and
Ma
,
X.
,
2012
, “
Analysis and Control of a Hyperchaotic System With Only One Nonlinear Term
,”
Nonlinear Dyn.
,
67
(
3
), pp.
1745
1752
.
19.
Chen
,
D.
,
Zhang
,
R.
,
Ma
,
X.
, and
Liu
,
S.
,
2012
, “
Chaotic Synchronization and Anti-Synchronization for a Novel Class of Multiple Chaotic Systems Via a Sliding Mode Control Scheme
,”
Nonlinear Dyn.
,
69
(1), pp.
35
55
.
20.
Guo
,
R.
,
2012
, “
Finite-Time Stabilization of a Class of Chaotic Systems Via Adaptive Control Method
,”
Commun. Nonlinear Sci. Numer. Simul.
,
17
(
1
), pp.
255
262
.
21.
Liu
,
Y.
,
Yang
,
Q.
, and
Pang
,
G.
,
2010
, “
A Hyperchaotic System From the Rabinovich System
,”
J. Comput. Appl. Math.
,
234
(
1
), pp.
101
113
.
22.
Pang
,
S.
, and
Liu
,
Y.
,
2011
, “
A New Hyperchaotic System From the Lü System and Its Control
,”
J. Comput. Appl. Math.
,
235
(
8
), pp.
2775
2789
.
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