We investigate the appearance of sharp pulses in the mean field of Kuramoto-type globally-coupled phase oscillator systems. In systems with exactly equidistant natural frequencies, self-organized periodic pulsations of the mean field, called mode locking, have been described recently as a new collective dynamics below the synchronization threshold. We show here that mode locking can appear also for frequency combs with modes of finite width, where the natural frequencies are randomly chosen from equidistant frequency intervals. In contrast to that, so-called coherence echoes, which manifest themselves also as pulses in the mean field, have been found in systems with completely disordered natural frequencies as a result of two consecutive stimulations applied to the system. We show that such echo pulses can be explained by a stimulation induced mode locking of a subpopulation representing a frequency comb. Moreover, we find that the presence of a second harmonic in the interaction function, which can lead to the global stability of the mode-locking regime for equidistant natural frequencies, can enhance the echo phenomenon significantly. The nonmonotonic behavior of echo amplitudes can be explained as a result of the linear dispersion within the self-organized mode-locked frequency comb. Finally, we investigate the effect of small periodic stimulations on oscillator systems with disordered natural frequencies and show how the global coupling can support the stimulated pulsation by increasing the width of locking plateaus.

1.
Y.
Kuramoto
, Chemical Oscillations, Waves, and Turbulence, Springer Series in Synergetics (Springer Verlag, Berlin, 1984).
2.
A.
Pikovsky
,
M.
Rosenblum
, and
J.
Kurths
,
Synchronization: A Universal Concept in Nonlinear Sciences
(
Cambridge University Press
,
2003
), Vol. 12.
3.
O. V.
Popovych
,
Y. L.
Maistrenko
, and
P. A.
Tass
,
Phys. Rev. E
71
,
065201(R)
(
2005
).
4.
S.
Eydam
and
M.
Wolfrum
,
Phys. Rev. E
96
,
052205
(
2017
).
5.
C.
Baesens
,
J.
Guckenheimer
,
S.
Kim
, and
R.
MacKay
,
Physica D
49
,
387
475
(
1991
).
6.
Y. L.
Maistrenko
,
O. V.
Popovych
,
O.
Burylko
, and
P. A.
Tass
,
Phys. Rev. Lett.
93
,
084102
(
2004
).
7.
Y. H.
Wen
,
M. R. E.
Lamont
,
S. H.
Strogatz
, and
A. L.
Gaeta
,
Phys. Rev. A
94
,
063843
(
2016
).
8.
H.
Taheri
,
P.
Del’Haye
,
A. A.
Eftekhar
,
K.
Wiesenfeld
, and
A.
Adibi
,
Phys. Rev. A
96
,
013828
(
2017
).
9.
E.
Ott
,
J. H.
Platig
,
T. M.
Antonsen
, and
M.
Girvan
,
Chaos
18
,
037115
(
2008
).
10.
B.
Kadomtsev
,
Sov. Phys. Usp.
11
,
328
(
1968
).
11.
E.
Ott
,
J. Plasma Phys.
4
(
3
),
471
476
(
1970
).
12.
R. W.
Gould
,
T. M.
O’Neil
, and
J. H.
Malmberg
,
Phys. Rev. Lett.
19
(
5
),
219
222
(
1967
).
13.
E. L.
Hahn
,
Phys. Rev.
80
(
4
),
580
(
1950
).
14.
H. Y.
Carr
and
E. M.
Purcell
,
Phys. Rev.
94
(
3
),
630
638
(
1954
).
15.
T.
Chen
,
M. R.
Tinsley
,
E.
Ott
, and
K.
Showalter
,
Phys. Rev. X
6
,
041054
(
2016
).
16.
G.
Karras
,
E.
Hertz
,
F.
Billard
,
B.
Lavorel
,
J.-M.
Hartmann
,
O.
Faucher
, and
I. S.
Averbukh
,
Phys. Rev. Lett.
114
(
15
),
153601
(
2015
).
17.
H.
Daido
,
Physica D
91
,
24
66
(
1996
).
18.
D.
Hansel
,
G.
Mato
, and
C.
Meunier
,
Europhys. Lett.
23
(
5
),
367
372
(
1993
).
19.
P.
Ashwin
,
C.
Bick
, and
O.
Burylko
,
Front. Appl. Math. Stat.
2
,
7
(
2016
).
20.
M.
Komarov
and
A.
Pikovsky
,
Phys. Rev. Lett.
111
,
204101
(
2013
).
21.
H.
Chiba
,
SIAM J. Appl. Dyn. Syst.
16
,
1235
1259
(
2017
).
22.
A.
Katok
and
B.
Hasselblatt
,
Introduction to the Modern Theory of Dynamical Systems
(
Cambridge University Press
,
1997
).
23.
M. H.
Jensen
,
P.
Bak
, and
T.
Bohr
,
Phys. Rev. Lett.
50
(
21
),
1637
1639
(
1983
).
24.
J.
Guckenheimer
and
P.
Holmes
,
Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields
(
Springer
,
1983
).
25.
R.
Brette
,
Set Valued Anal.
11
(
4
),
359
371
(
2003
).
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