We investigate synchronization of time varying networks and stability conditions. We derive interesting relations between the critical coupling constants for synchronization and switching times for time-varying and time average networks. The relations are based on the additive property of Lyapunov exponents and are verified experimentally in electronic circuit.

1.
S. H.
Strogatz
,
Nature
410
,
268
(
2001
).
2.
R. E.
Mirollo
and
S. H.
Strogatz
,
SIAM J. Appl. Math.
50
,
1645
(
1990
).
3.
R.
Albert
and
A. L.
Barabasi
,
Rev. Mod. Phys.
74
,
47
(
2002
).
4.
H.
Cheté
and
P.
Manneville
,
Europhys. Lett.
17
,
219
(
1992
).
5.
P. M.
Gede
.
Phys. Rev. E.
54
,
64
(
1996
).
6.
S. C.
Manrubia
and
A. S.
Mikhailov
,
Phys. Rev. E
60
,
1579
(
1999
).
7.
P. M.
Gede
and
C. K.
Hu
,
Phys. Rev. E
62
,
6409
(
2000
).
8.
S.
Sinha
,
Phys. Rev. E
66
,
016209
(
2002
).
9.
S.
Jalan
and
R. E.
Amritkar
,
Phys. Rev. Lett.
90
,
410
(
2003
).
10.
S.
Jalan
,
R. E.
Amritkar
, and
C. K.
Hu
,
Phys. Rev. E
72
,
016211
(
2005
);
S.
Jalan
,
R. E.
Amritkar
, and
C. K.
Hu
,
Phys. Rev. E
72
,
016212
(
2005
).
11.
J. D.
Skufka
and
E. M.
Bolt
,
Math. Biosci. Eng.
1
,
347
(
2004
).
12.
D. J.
Stilwell
,
E. M.
Bollt
, and
D. G.
Roberson
,
SIAM J. Appl. Dyn. Syst.
5
,
140
(
2006
).
13.
R. E.
Amritkar
and
C. K.
Hu
,
Chaos
16
,
015117
(
2006
).
14.
I. V.
Belykh
,
V. N.
Belykh
, and
M.
Hasler
,
Physica D
195
,
188
(
2004
).
15.
S.
Boccaletti
,
D. U.
Heang
,
M.
Chavez
,
A.
Amann
,
J.
Kurths
, and
L. M.
Pecora
,
Phys. Rev. E
74
,
016012
(
2006
).
16.
R.
Zhang
,
M.
Hu
, and
Z.
Xu
,
Physica D
368
,
276
(
2007
).
17.
18.
19.
S. K.
Dana
,
B.
Blasius
, and
J.
Kurths
,
Chaos
16
,
023111
(
2006
).
20.
P. K.
Roy
,
S.
Chakraborty
, and
S. K.
Dana
,
Chaos
13
,
342
(
2003
).
21.
L. M.
Pecora
and
T. L.
Carroll
,
Phys. Rev. Lett.
80
,
2109
(
1998
).
22.
J.
Friedrich
and
W.
Kinzel
,
J. Comput. Neurosci.
27
,
65
(
2009
).
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