We study the two-dimensional map modelling neuron known as the Chialvo map. We consider Chialvo maps on a one-dimensional lattice in the presence of quenched disorder. We study the various dynamical phases for various values of coupling strength and quenched disorder. We observe the ‘chimera-like’ states where different sites reach different qualitative dynamical behavior. Even in the strong coupling, we observe the ‘chimera-like’ states. Thus the neurons cannot be identical or uniform. The coupling is purely local.
REFERENCES
1.
K.
Schneider
and J.D.
Murray
: Mathematical biology. biomathematics vol. 19. springer-verlag 1989
, 767 s., 292 abb., dm 98, —. Biometrical Journal
, 33
(3
):377
–378
, 1991
.2.
L.
Glass
and M. C.
Mackey
. From clocks to chaos: The rhythms of life
. Princeton University Press
, 1988
.3.
A. T.
Winfree
and J. J.
Tyson
. When time breaks down: The three-dimensional dynamics of electrochemical waves and cardiac arrhythmias
. Physics Today
, 41
(12
):107
, 1988
.4.
J.
Rinzel
and G. B.
Ermentrout
. Analysis of neural excitability and oscillations
. Methods in neuronal modeling
, 2
:251
–292
, 1998
.5.
6.
E. M.
Izhikevich
and R.
FitzHugh
. Fitzhugh-nagumo model
. Scholarpedia
, 1
(9
):1349
, 2006
.7.
A. N.
Burkitt
. A review of the integrate-and-fire neuron model: I. homogeneous synaptic input
. Biological cybernetics
, 95
:1
–19
, 2006
.8.
J. M.
Bower
, H.
Cornelis
, and D.
Beeman
. GENESIS, The GEneral NEural SImulation System
, pages 1
–8
. Springer
New York, New York, NY
, 2013
.9.
D. R.
Chialvo
and A. V.
Apkarian
. Modulated noisy biological dynamics: three examples
. Journal of Statistical Physics
, 70
:375
–391
, 1993
.10.
D. R.
Chialvo
. Generic excitable dynamics on a two-dimensional map
. Chaos, Solitons & Fractals
, 5
(3-4
):461
–479
, 1995
.11.
B.
Cazelles
, M.
Courbage
, and M
Rabinovich
. Anti-phase regularization of coupled chaotic maps modelling bursting neurons
. Europhysics Letters
, 56
(4
):504
, 2001
.12.
N. F
Rulkov
. Regularization of synchronized chaotic bursts
. Physical Review Letters
, 86
(1
):183
, 2001
.13.
K. V.
Andreev
and L. V.
Krasichkov
. Using of phenomenological piecewise continuous map for modeling of neurons behaviour.
arXiv: Chaotic Dynamics, 2002
.14.
M.
Girardi-Schappo
, M. H. R.
Tragtenberg
, and O.
Kinouchi
. A brief history of excitable map-based neurons and neural networks
. Journal of neuroscience methods
, 220
(2
):116
–130
, 2013
.15.
M. P. K.
Jampa
, A. R.
Sonawane
, P. M.
Gade
, and S.
Sinha
. Synchronization in a network of model neurons
. Physical Review E
, 75
(2
):026215
, 2007
.16.
S. S.
Muni
, H.O.
Fatoyinbo
, and I.
Ghosh
. Dynamical effects of electromagnetic flux on chialvo neuron map: Nodal and network behaviors
. International Journal of Bifurcation and Chaos
, 32
, 07
2022
.17.
D. J.
Watts
and S. H.
Strogatz
. Collective dynamics of ‘small-world’networks
. nature
, 393
(6684
):440
–442
, 1998
.18.
S. A.
Pandit
and R. E.
Amritkar
. Characterization and control of small-world networks
. Physical Review E
, 60
(2
):R1119
, 1999
.19.
F.
Parastesh
, S.
Jafari
, H.
Azarnoush
, Z.
Shahriari
, Z.
Wang
, S.
Boccaletti
, and M.
Perc
. Chimeras. Physics Reports
, 898
:1
–114
, 2021
.20.
Y.
Kuramoto
and D.
Battogtokh
. Coexistence of coherence and incoherence in nonlocally coupled phase oscillators: A soluble case
. J. Nonlin. Phenom. Complex Syst.
, 5
, 12
2002
.21.
D. M.
Abrams
and S. H.
Strogatz
. Chimera states for coupled oscillators
. Physical review letters
, 93
(17
):174102
, 2004
.22.
L. V.
Gambuzza
, A.
Buscarino
, S.
Chessari
, L.
Fortuna
, R.
Meucci
, and M.
Frasca
. Experimental investigation of chimera states with quiescent and synchronous domains in coupled electronic oscillators
. Phys. Rev. E
, 90
:032905
, Sep 2014
.23.
M. R.
Tinsley
, S.
Nkomo
, and K.
Showalter
. Chimera and phase-cluster states in populations of coupled chemical oscillators
. Nature Physics
, 8
(9
):662
–665
, 2012
.24.
I.
Omelchenko
, Y.
Maistrenko
, P.
Hovel
, and E.
Scholl
. Loss of coherence in dynamical networks: Spatial chaos and chimera states
. Phys. Rev. Lett.
, 106
:234102
, Jun 2011
.25.
S.
Majhi
, B. K.
Bera
, D.
Ghosh
, and M.
Perc
. Chimera states in neuronal networks: A review
. Physics of life reviews
, 28
:100
–121
, 2019
.26.
C. R.
Laing
. Chimera states in heterogeneous networks
. Chaos: An Interdisciplinary Journal of Nonlinear Science
, 19
(1
):013113
, 2009
.27.
C. R.
Laing
. The dynamics of chimera states in heterogeneous kuramoto networks
. Physica D: Nonlinear Phenomena
, 238
(16
):1569
–1588
, 2009
.28.
E. A.
Martens
, C.
Bick
, and M. J.
Panaggio
. Chimera states in two populations with heterogeneous phase-lag
. Chaos: An Interdisciplinary Journal of Nonlinear Science
, 26
(9
):094819
, 2016
.29.
E.V.
Rybalova
, T.E.
Vadivasova
, G.I.
Strelkova
, V. S.
Anishchenko
, and A.S.
Zakharova
. Forced synchronization of a multilayer hetero-geneous network of chaotic maps in the chimera state mode
. Chaos: an interdisciplinary journal of nonlinear science
, 29
(3
):033134
, 2019
.30.
L.A.
Smirnov
, M.I.
Bolotov
, G.V.
Osipov
, and A.
Pikovsky
. Disorder fosters chimera in an array of motile particles
. Physical Review E
, 104
(3
):034205
, 2021
.31.
H.
Hong
, K.
Yeo
, and H. Keun
Lee
. Coupling disorder in a population of swarmalators
. Physical Review E
, 104
(4
):044214
, 2021
.32.
H.
Hong
and E. A.
Martens
. First-order like phase transition induced by quenched coupling disorder
. Chaos: An Interdisciplinary Journal of Nonlinear Science
, s32
(6
):063125
, 2022
.33.
A. K.
Malchow
, I.
Omelchenko
, E.
Scholl
, and P.
Hovel
. Robustness of chimera states in nonlocally coupled networks of nonidentical logistic maps
. Physical Review E
, 98
(1
):012217
, 2018
This content is only available via PDF.
© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
