We have studied the effects of perturbations on the cat's cerebral cortex. According to the literature, this cortex structure can be described by a clustered network. This way, we construct a clustered network with the same number of areas as in the cat matrix, where each area is described as a sub-network with a small-world property. We focus on the suppression of neuronal phase synchronisation considering different kinds of perturbations. Among the various controlling interventions, we choose three methods: delayed feedback control, external time-periodic driving, and activation of selected neurons. We simulate these interventions to provide a procedure to suppress undesired and pathological abnormal rhythms that can be associated with many forms of synchronisation. In our simulations, we have verified that the efficiency of synchronisation suppression by delayed feedback control is higher than external time-periodic driving and activation of selected neurons of the cat's cerebral cortex with the same coupling strengths.

1.
G.
Buzsaki
,
Rhythms of the Brain
(
Oxford University Press
,
Oxford
,
2006
).
2.
J. S.
Lund
,
T.
Yoshioka
, and
J. B.
Levitt
, “
Comparison of intrinsic connectivity in different areas of macaque monkey cerebral
,”
Cereb. Cortex
3
,
148
162
(
1993
).
3.
E. J.
Izquierdo
and
R. D.
Beer
, “
Connecting a connectome to behavior: An ensemble of neuroanatomical models of C. elegans klinotaxis
,”
PLoS One Comput. Biol.
9
,
e1002890
(
2013
).
4.
J. W.
Scannell
,
C.
Blakemore
, and
M. P.
Young
, “
Analysis of connectivity in the cat cerebral cortex
,”
J. Neurosci.
15
,
1463
1483
(
1995
).
5.
J. W.
Scannell
and
M. P.
Young
, “
The connectional organization of neural systems in the cat cerebral cortex
,”
Curr. Biol.
3
,
191
200
(
1993
).
6.
J.
Gómez-Gardeñes
,
G.
Zamora-López
,
Y.
Moreno
, and
A.
Arenas
, “
From modular to centralized organization of synchronization in functional areas of the cat cerebral cortex
,”
PLoS One
5
,
e12313
(
2010
).
7.
C. C.
Hilgetag
,
G. A.
Burns
,
M.
Oneill
,
J. W.
Scannell
, and
M. P.
Young
, “
Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat
,”
Philos. Trans. R. Soc. London B
355
,
91
100
(
2000
).
8.
C.
Zhou
,
L.
Zemanová
,
G.
Zamora
,
C. C.
Hilgetag
, and
J.
Kurths
, “
Hierarchical organization unveiled by functional connectivity in complex brain networks
,”
Phys. Rev. Lett.
97
,
238103
(
2006
).
9.
L.
Zemanová
,
C.
Zhou
, and
J.
Kurths
, “
Structural and functional clusters of complex brain networks
,”
Physica D
224
,
202
212
(
2006
).
10.
D.
Watts
,
J.
Duncan
, and
S. H.
Strogatz
, “
Collective dynamics of small-world networks
,”
Nature
393
,
440
442
(
1998
).
11.
C. J.
Stam
,
B. F.
Jones
,
G.
Nolte
,
M.
Breakspear
, and
Ph.
Scheltens
, “
Small-world networks and functional connectivity in Alzheimer's disease
,”
Cereb. Cortex
17
,
92
99
(
2007
).
12.
T. I.
Netoff
,
R.
Clewley
,
S.
Arno
,
T.
Keck
, and
J. A.
White
, “
Epilepsy in small-world networks
,”
J. Neurosci.
24
,
8075
8083
(
2004
).
13.
A. L.
Hodgkin
and
A. F.
Huxley
, “
A quantitative description of membrane current and its application to conduction and excitation in nerve
,”
J. Physiol.
117
,
500
544
(
1952
).
14.
J. L.
Hindmarsh
and
R. M.
Rose
, “
A model of neuronal bursting using three coupled first order differential equations
,”
Proc. R. Soc. London B
221
,
87
102
(
1984
).
15.
N. F.
Rulkov
, “
Regularization of synchronized chaotic bursts
,”
Phys. Rev. Lett.
86
,
183
186
(
2001
).
16.
B.
Ibarz
,
J. M.
Casado
, and
M. A. F.
Sanjuán
, “
Map-based models in neuronal dynamics
,”
Phys. Rep.
501
,
1
74
(
2011
).
17.
M.
Dhamala
,
V. K.
Jirsa
, and
M.
Ding
, “
Transitions to synchrony in coupled bursting neurons
,”
Phys. Rev. Lett.
92
,
028101
(
2004
).
18.
C. A. S.
Batista
,
E. L.
Lameu
,
A. M.
Batista
,
S. R.
Lopes
,
T.
Pereira
,
G.
Zamora-López
,
J.
Kurths
, and
R. L.
Viana
, “
Phase synchronization of bursting neurons in clustered small-world networks
,”
Phys. Rev. E
86
,
016211
(
2012
).
19.
E. L.
Lameu
,
F. S.
Borges
,
R. R.
Borges
,
A. M.
Batista
,
M. S.
Baptista
, and
R. L.
Viana
, “
Network induces burst synchronisation in cat cerebral cortex
,”
Commun. Nonlinear Sci. Numer. Simul.
34
,
45
54
(
2016
).
20.
E. L.
Lameu
,
C. A. S.
Batista
,
A. M.
Batista
,
K.
Iarosz
,
R. L.
Viana
,
S. R.
Lopes
, and
J.
Kurths
, “
Suppression of bursting synchronization in clustered scale-free (rich-club) neuronal networks
,”
Chaos
22
,
043149
(
2012
).
21.
Q. Y.
Wang
,
Z. S.
Duan
,
L.
Huang
,
G. R.
Chen
, and
Q. S.
Lu
, “
Pattern formation and firing synchronization in networks of map neurons
,”
New J. Phys.
9
,
383
(
2007
).
22.
A.
Koseska
,
E.
Volkov
, and
J.
Kurths
, “
Oscillation quenching mechanisms: Amplitude vs. oscillation death
,”
Phys. Rep.
531
,
173
199
(
1999
).
23.
J.
Fell
and
N.
Axmacher
, “
The role of phase synchronization in memory processes
,”
Nat. Rev. Neurosci.
12
,
105
118
(
2011
).
24.
P. R.
Roelfsema
,
A. K.
Engel
,
P.
König
, and
W.
Singer
, “
Visuomotor integration is associated with zero time-lag synchronization among cortical areas
,”
Nature
385
,
157
161
(
1997
).
25.
M. V.
Ivanchenko
,
G. V.
Osipov
,
V. D.
Shalfeev
, and
J.
Kurths
, “
Phase synchronization in ensembles of bursting oscillators
,”
Phys. Rev. Lett.
93
,
134101
(
2004
).
26.
N.
Axmacher
,
F.
Mormann
,
G.
Fernández
,
C. E.
Elger
, and
J.
Fell
, “
Memory formation by neuronal synchronization
,”
Brain Res. Rev.
52
,
170
182
(
2006
).
27.
P. J.
Uhlhaas
and
W.
Singer
, “
Neural synchrony in brain disorders: Relevance for cognitive dysfunctions and pathophysiology
,”
Neuron
52
,
155
168
(
2006
).
28.
C. C.
Chen
,
V.
Litvak
,
T.
Gilbertson
,
A.
Kühn
,
C. S.
Lu
,
S. T.
Lee
,
C. H.
Tsai
,
S.
Tisch
,
P.
Limousin
,
M.
Hariz
, and
P.
Brown
, “
Excessive synchronization of basal ganglia neurons at 20 Hz slows movement in Parkinson's disease
,”
Exp. Neurol.
205
,
214
221
(
2007
).
29.
R.
Levy
,
W. D.
Hutchison
,
A. M.
Lozano
, and
J. O.
Dostrovsky
, “
High-frequency synchronization of neuronal activity in the subthalamic nucleus of Parkinsonian patients with limb tremor
,”
J. Neurosci.
20
,
7766
7775
(
2000
).
30.
M. G.
Rosenblum
and
A. S.
Pikowsky
, “
Delayed feed back control of collective synchrony: An approach to suppression of pathological brain rhythms
,”
Phys. Rev. E
70
,
041904
(
2004
).
31.
C. A. S.
Batista
,
S. R.
Lopes
,
R. L.
Viana
, and
A. M.
Batista
, “
Delayed feedback control of bursting synchronization in a scale-free neuronal network
,”
Neural Networks
23
,
114
124
(
2010
).
32.
C. A. S.
Batista
,
R. L.
Viana
,
F. A. S.
Ferrari
,
S. R.
Lopes
,
A. M.
Batista
, and
J. C. P.
Coninck
, “
Control of bursting synchronization in networks of Hodgkin-Huxley-type neurons with chemical synapses
,”
Phys. Rev. E
87
,
042713
(
2013
).
33.
D. E. J.
Linden
,
I.
Habes
,
S. J.
Johnston
,
S.
Linden
,
R.
Tatineni
,
L.
Subramanian
,
B.
Sorger
,
D.
Healy
, and
R.
Goebel
, “
Real-time self-regulation of emotion networks in patients with depression
,”
PLoS One
7
,
e38115
(
2012
).
34.
R. P.
Lesser
, “
Electrical stimulation depresses epileptiform activity
,”
Epilepsy Curr.
3
,
137
138
(
2003
).
35.
X.
Han
and
E. S.
Boyden
, “
Multiple-color optical activation, silencing, and desynchronization of neural activity, with single-spike temporal resolution
,”
PLoS One
2
,
e299
(
2007
).
36.
M. E.
Newman
and
D. J.
Watts
, “
Renormalization group analysis of the small-world network model
,”
Phys. Lett. A
263
,
341
346
(
1999
).
37.
Y.
Kuramoto
,
Chemical Oscillations, Waves, and Turbulence
(
Springer Verlag
,
Berlin
,
1984
).
38.
M. G.
Rosenblum
and
A. S.
Pikovsky
, “
Controlling synchronization in an ensemble of globally coupled oscillators
,”
Phys. Rev. Lett.
92
,
114102
(
2004
).
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