We consider spatially localized spiking activity patterns, so-called bumps, in ensembles of bistable spiking oscillators. The bistability consists in the coexistence of self-sustained spiking dynamics and a quiescent steady-state regime. We show numerically that the processes of growth or contraction of such patterns can be controlled by varying the intensity of multiplicative noise. In particular, the effect of noise is monotonic in an ensemble of coupled Hindmarsh–Rose oscillators. On the other hand, in another model proposed by Semenov et al. [Semenov et al., Phys. Rev. E 93, 052210 (2016)], a resonant noise effect is observed. In that model, stabilization of activity bump expansion is achieved at an appropriate noise level, and the noise effect reverses with a further increase in noise intensity. Moreover, we show the constructive role of nonlocal coupling that allows us to save domains and fronts being totally destroyed due to the action of noise in the case of local coupling.

1.
D.
Papo
and
J.
Buldú
, “
Brain synchronizability, a false friend
,”
NeuroImage
196
,
195
199
(
2019
).
2.
Neural Fields, edited by S. Coombes, P. Graben, R. Potthast, and J. Wright (Springer, 2014).
3.
A.
Compte
,
N.
Brunel
,
P.
Goldman-Rakic
, and
X.-J.
Wang
, “
Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model
,”
Cereb. Cortex
10
,
910
923
(
2000
).
4.
K.
Wimmer
,
D.
Nykamp
,
C.
Constantinidis
, and
A.
Compte
, “
Bump attractor dynamics in prefrontal cortex explains behavioral precision in spatial working memory
,”
Nat. Neurosci.
17
,
431
439
(
2014
).
5.
J.
Taube
, “
Head direction cells and the neurophysiological basis for a sence of direction
,”
Prog. Neurobiol.
55
,
225
256
(
1998
).
6.
P.
Sharp
,
H.
Blair
, and
J.
Cho
, “
The anatomical and computational basis of the rat head-direction cell signal
,”
Trends Neurosci.
24
,
289
294
(
2001
).
7.
P.
Blomquist
,
J.
Wyller
, and
G.
Einevoll
, “
Localized activity patterns in two-population neuronal networks
,”
Physica D
206
,
180
212
(
2005
).
8.
M.
Yousaf
,
B.
Kriener
,
J.
Wyller
, and
G.
Einevoll
, “
Generation and annihilation of localized persistent-activity states in a two-population neural-field model
,”
Neural Netw.
46
,
75
90
(
2013
).
9.
J.
Rubin
and
A.
Bose
, “
Localized activity patterns in excitatory neuronal networks
,”
Netw. Comput. Neural Syst.
15
,
133
158
(
2004
).
10.
J. E.
Rubin
, “
Surprising effects of synaptic excitation
,”
J. Comput. Neurosci.
18
,
333
342
(
2005
).
11.
J.
Rubin
and
A.
Bose
, “
The geometry of neuronal recruitment
,”
Physica D
221
,
37
57
(
2006
).
12.
C.
Laing
, “
Exact neural fields incorporating gap junctions
,”
SIAM J. Appl. Dyn. Syst.
14
,
1899
1929
(
2015
).
13.
D.
Avitabile
and
K. A.
Wedgwood
, “
Macroscopic coherent structures in a stochastic neural network: From interface dynamics to coarse-grained bifurcation analysis
,”
Math. Biol.
75
,
885
928
(
2017
).
14.
H.
Schmidt
and
D.
Avitabile
, “
Bumps and oscillons in networks of spiking neurons
,”
Chaos
30
,
033133
(
2020
).
15.
D.
Avitabile
and
H.
Schmidt
, “
Snakes and ladders in an inhomogeneous neural field model
,”
Physica D
294
,
24
36
(
2015
).
16.
F.
Schlögl
, “
Chemical reaction models for non-equilibrium phase transitions
,”
Z. Phys.
253
,
147
161
(
1972
).
17.
F.
Schlögl
,
C.
Escher
, and
R.
Berry
, “
Fluctuations in the interface between two phases
,”
Phys. Rev. A
27
,
2698
2704
(
1983
).
18.
“Control of chemical wave propagation,” in Engineering of Chemical Complexity II, edited by A. Mikhailov and G. Ertl (World Scientific, 2014), pp. 185–207.
19.
E.
Schöll
, Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors, Nonlinear Science Series (Cambridge University Press, 2001), Vol. 10.
20.
Y.
Zel’dovich
and
D.
Frank-Kamenetskii
, “
Theory of uniform flame propagation
,”
Dokl. Akad. Nauk SSSR
19
,
693
798
(
1938
).
21.
B.
Yurke
,
A.
Pagellis
,
I.
Chuang
, and
N.
Turok
, “
Coarsening in nematic liquid crystals
,”
Physica B
178
,
56
72
(
1992
).
22.
A.
Bray
, “
Theory of phase-ordering kinetics
,”
Adv. Phys.
43
,
357
459
(
1994
).
23.
L.
Cugliandolo
, “
Topics in coarsening phenomena
,”
Physica A
389
,
4360
4373
(
2010
).
24.
F.
Caccioli
,
S.
Franz
, and
M.
Marsili
, “
Ising model with memory: Coarsening and persistence properties
,”
J. Stat. Mech. Theory Exp.
2008
,
P07006
.
25.
J.
Denholm
and
S.
Redner
, “
Topology-controlled Potts coarsening
,”
Phys. Rev. E
99
,
062142
(
2019
).
26.
Y.
Goh
and
R.
Jacobs
, “
Coarsening dynamics of granular heaplets in tapped granular layers
,”
New J. Phys.
4
,
81.1
81.9
(
2002
).
27.
C.
Zhang
,
L.
Yu
, and
H.
Wang
, “
Kinetic analysis for high-temperature coarsening of γ phase in Ni-based superalloy GH4169
,”
Materials
12
,
2096
(
2019
).
28.
L.
Zhang
,
Q.
Liu
, and
P.
Crozier
, “
Light induced coarsening of metal nanoparticles
,”
J. Mater. Chem. A
7
,
11756
11763
(
2019
).
29.
P.
Geslin
,
M.
Buchet
,
T.
Wada
, and
H.
Kato
, “
Phase-field investigation of the coarsening of porous structures by surface diffusion
,”
Phys. Rev. Mater.
3
,
083401
(
2019
).
30.
G.
Giacomelli
,
F.
Marino
,
M.
Zaks
, and
S.
Yanchuk
, “
Coarsening in a bistable system with long-delayed feedback
,”
Europhys. Lett.
99
,
58005
(
2012
).
31.
F.
Marino
,
G.
Giacomelli
, and
S.
Barland
, “
Front pinning and localized states analogues in long-delayed bistable systems
,”
Phys. Rev. Lett.
112
,
103901
(
2014
).
32.
J.
Javaloyes
,
T.
Ackemann
, and
A.
Hurtado
, “
Arrest of domain coarsening via antiperiodic regimes in delay systems
,”
Phys. Rev. Lett.
115
,
203901
(
2015
).
33.
V.
Semenov
and
Y.
Maistrenko
, “
Dissipative solitons for bistable delayed-feedback systems
,”
Chaos
28
,
101103
(
2018
).
34.
U.
Dobramysl
,
M.
Mobilia
,
M.
Pleimling
, and
U.
Täuber
, “
Stochastic population dynamics in spatially extended predator–prey systems
,”
J. Phys. A
51
,
063001
(
2018
).
35.
S.
Ruschel
and
S.
Yanchuk
, “
Delay-induced switched states in a slow-fast system
,”
Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci.
377
,
20180118
(
2019
).
36.
T.
Vadivasova
,
A.
Slepnev
, and
A.
Zakharova
, “
Control of inter-layer synchronization by multiplexing noise
,”
Chaos
30
,
091101
(
2020
).
37.
M.
Masoliver
,
N.
Malik
,
E.
Schöll
, and
A.
Zakharova
, “
Coherence resonance in a network of FitzHugh-Nagumo systems: Interplay of noise, time-delay, and topology
,”
Chaos
27
,
101102
(
2017
).
38.
T.
Bogatenko
and
V.
Semenov
, “
Coherence resonance in an excitable potential well
,”
Phys. Lett. A
382
,
2645
2649
(
2018
).
39.
N.
Semenova
and
A.
Zakharova
, “
Weak multiplexing induces coherence resonance
,”
Chaos
28
,
051104
(
2018
).
40.
A.
Pisarchik
,
V.
Maksimenko
,
A.
Andreev
,
N.
Frolov
,
V.
Makarov
,
M.
Zhuravlev
,
A.
Runnova
, and
A.
Hramov
, “
Coherent resonance in the distributed cortical network during sensory information processing
,”
Sci. Rep.
9
,
18325
(
2019
).
41.
M.
Yamakou
and
J.
Jost
, “
Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network
,”
Phys. Rev. E
100
,
022313
(
2019
).
42.
M.
Masoliver
,
C.
Masoller
, and
A.
Zakharova
, “
Control of coherence resonance in multiplex neural networks
,”
Chaos, Solitons Fractals
145
,
110666
(
2021
).
43.
V.
Semenov
and
A.
Zakharova
, “
Multiplexing-based control of stochastic resonance
,”
Chaos
32
,
121106
(
2022
).
44.
M.
Yamakou
and
T.
Tran
, “
Lévy noise-induced self-induced stochastic resonance in a memristive neuron
,”
Nonlinear Dyn.
107
,
2847
2865
(
2021
).
45.
A.
Engel
, “
Noise-induced front propagation in a bistable system
,”
Phys. Lett. A
113
,
139
142
(
1985
).
46.
J.
Garcia-Ojalvo
and
J.
Sancho
,
Noise in Spatially Extended Systems
(
Springer
,
1999
).
47.
V.
Méndez
,
I.
Llopis
,
D.
Campos
, and
W.
Horsthemke
, “
Effect of environmental fluctuations on invasion fronts
,”
J. Theor. Biol.
281
,
31
38
(
2011
).
48.
S.
Tsuji
,
T.
Ueta
,
H.
Kawakami
,
H.
Fujii
, and
K.
Aihara
, “
Bifurcations in two-dimensional Hindmarsh-Rose type model
,”
Int. J. Bifurcat. Chaos
17
,
985
998
(
2007
).
49.
R.
Mannella
, “
Integration of stochastic differential equations on a computer
,”
Int. J. Modern Phys. C
13
,
1177
1194
(
2002
).
50.
V.
Semenov
,
A.
Neiman
,
T.
Vadivasova
, and
V.
Anishchenko
, “
Noise-induced transitions in a double-well oscillator with nonlinear dissipation
,”
Phys. Rev. E
93
,
052210
(
2016
).
51.
V.
Semenov
, “
Noise-induced transitions in a double-well excitable oscillator
,”
Phys. Rev. E
95
,
052205
(
2017
).
52.
V.
Semenov
, “
Self-oscillation excitation under condition of positive dissipation in a state-dependent potential well
,”
Chaos, Solitons Fractals
116
,
358
364
(
2018
).
53.
F.
da Silva
,
W.
Blanes
,
S.
Kalitzin
,
J.
Parra
,
P.
Suffczynski
, and
D.
Velis
, “
Dynamical diseases of brain systems: Different routes to epileptic seizures
,”
IEEE Trans. Biomed. Eng.
50
,
540
548
(
2003
).
54.
P.
Suffczynski
,
S.
Kalitzin
, and
F.
da Silva
, “
Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network
,”
Neuroscience
126
,
467
484
(
2004
).
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