Abstract
We use extensive computer simulations to study synchronization phenomena in networks of biological neurons. Each individual neuron is modeled using the leaky integrate-and-fire (LIF) scheme, while many neurons are coupled nonlocally in a network. In this system chimera states develop, which are complex states consisting of coexisting synchronous and asynchronous network areas. We study the influence of the network size on the properties and the form of chimera states. We show that for constant coupling strength, the number of the synchronous/asynchronous domains depends quantitatively on the coupling ratio. This dependence allows to extract synchronization properties in large ensembles of neurons after extrapolating from simulations of small networks. Since computer simulations of even small neuron networks are highly demanding in memory and CPU time, this property is particularly important in view of the large number of neurons involved in any cognitive function. In total, the number of neurons in the human brain is of the order of 1010, and each of them is connected with an average of 103 other neurons.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Abott LF (2007) Lapicques introduction of the integrate-and-fire model neuron (1907). Biol Cybern 97:337
Abrams DM, Strogatz SH (2004) Chimera states for coupled oscillators. Phys Rev Lett 93:174102
Andrzejak RG, Rummel C, Mormann F, Schindler K (2016) All together now: analogies between chimera state collapses and epileptic seizures. Sci Rep 6:23000
Bera BK, Ghosh D, Lakshmanan M (2016) Chimera states in bursting neurons. Phys Rev E 93:012205
Brunel N, van Rossum MC (1999) Lapicque’s 1907 paper: from frogs to integrate-and-fire. Brain Res Bull 50:303304
Cobb SR, Buhl EH, Halasy K, Paulsen O, Somogyi P (1995) Synchronization of neuronal activity in hippocampus by individual GABAergic interneurons. Nature 378:75–78
Essaki Arumugam M, Spano ML (2015) A chimeric path to neuronal synchronization. Chaos 25(1):4905856
Fell J, Axmacher N (2011) The role of phase synchronization in memory processes. Nat Rev Neurosci 12:105–118
Haken H (2008) Springer Series on Synergetics. Brain dynamics, an introduction to models and simulations. Springer-Verlag, Berlin
Hizanidis VK, Bezerianos A, Bountis T (2014) Chimera states in networks of nonlocally coupled Hindmarsh-Rose neuron models. Int J Bifurc Chaos 24(03):1450030
Hizanidis J, Kouvaris NE, Zamora-Lopez G, az-Guilera AD, Antonopoulos CG (2016) Chimera-like states in modular neural networks. Sci Rep 6:19845
Izhikevich EM (2007) Dynamical systems in neuroscience: the geometry of excitability and bursting. The MIT Press, Cambridge
Kasimatis T, Hizanidis J, Provata A (2018) Three-dimensional chimera patterns in networks of spiking neuron oscillators. Phys Rev E 97:052213
Kuramoto Y, Battogtokh D (2002) Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. Nonlinear Phenom Complex Syst 5:380
Li W-K, Hausknecht MJ, Stone P, Mauk MD (2013) Using a million cell simulation of the cerebellum: network scaling and task generality. Neural Netw 47:95–102
Lucioli S, Politi A (2010) Irregular collective behavior of heterogeneous neural networks. Phys Rev E 105:158104
Maistrenko Y, Sudakov O, Osiv O, Maistrenko V (2015) Chimera states in three dimensions. New J Phys 17:073037
Maistrenko V, Sudakov O, Osiv O, Maistrenko Y (2017) Multiple scroll wave chimera states. Eur Phys J Spec Top 226:1867–1881
Majhi S, Perc M, Ghosh D (2016) Chimera states in uncoupled neurons induced by a multilayer structure. Sci Rep 6:39033
Mormann K, Lehnertz PD, Elger CE (2000) Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients. Physica D 144:358
Mormann T, Kreuz RG, Andrzejak P, David KL, Elger CE (2003) Epileptic seizures are preceded by a decrease in synchronization. Epilepsy Res 53:173–185
Olmi S, Politi A, Torcini A (2010) Collective chaos in pulse-coupled neural networks. Europhys Lett 92:60007
Omelchenko I, Omel’chenko OE, Hövel P, Schöll E (2013) When nonlocal coupling between oscillators becomes stronger: patched synchrony or multichimera states. Phys Rev Lett 110:224101
Omelchenko I, Provata A, Hizanidis J, Schöll E, Hövel P (2015) Robustness of chimera states for coupled FitzHugh-Nagumo oscillators. Phys Rev E 91:022917
Panaggio J, Abrams D (2015) Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators. Nonlinearity 28:R67
Plerou A, Vlamos P (2015) Evaluation of mathematical cognitive functions with the use of EEG brain imaging. In: Experimental multimedia Systems for interactivity and strategic innovation. IGI Global, Hershey, PA. pp 284–306
Plerou A, Vlamos P, Margetaki A (2017) EEG analysis of the neurofeedback training effect in algorithmic thinking. Adv Exp Med Biol 988:313–324
Psiha M, Vlamos P (2015) Modeling neural circuits in Parkinsons disease. Adv Exp Med Biol 822:139–147
Rattenborg C, Amlaner CJ, Lima SL (2000) Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep. Neurosci Biobehav Rev 24:817
Rattenborg C, Martinez-Gonzalez D, Lesku JA, Scriba M (2008) A bird’s eye view of sleep. Science 322:527
Schmidt A, Kasimatis T, Hizanidis J, Provata A, Hövel P (2017) Chimera patterns in two-dimensional networks of coupled neurons. Phys Rev E 95:032224
Schöll E (2016) Synchronization patterns and chimera states in complex networks: interplay of topology and dynamics. Eur Phys J Spec Top 225:891919
Tsigkri-DeSmedt ND, Hizanidis J, Hövel P, Provata A (2016) Multi-chimera states and transitions in the leaky integrate-and-fire model with nonlocal coupling and hierarchical connectivity. Eur Phys J Spec Top 225:11491164
Tsigkri-DeSmedt ND, Hizanidis J, Hövel P, Provata A (2015) Multi-chimera states in the leaky integrate-and-fire model. Procedia Comput Sci 66:13
Tsigkri-DeSmedt ND, Hizanidis J, Schöll E, Hövel P, Provata A (2017) Chimera states in the leaky integrate-and-fire model: effects of reflecting connectivity. Eur Phys J B 90:139
Tsigkri-DeSmedt ND, Koulierakis I, Karakos G, Provata A (2018) Synchronization patterns in LIF neuron networks: merging nonlocal and diagonal connectivity. Eur Phys J B 91:305
Vasalou EDH, Henson MA (2009) Small-world network models of intercellular coupling predict enhanced synchronization in the suprachiasmatic nucleus. J Biol Rhythm 24:243–254
Vuksanovic V, Hövel P (2014) Functional connectivity of distant cortical regions: role of remote synchronization and symmetry in interactions. NeuroImage 97:1
Vuksanovic V, Hövel P (2015) Dynamic changes in network synchrony reveal resting-state functional networks. Chaos 25:023116
Wu Z-M, Cheng H-Y, Feng Y, Li H-H, Dai Q-L, Yang J-Z (2018) Chimera states in bipartite networks of FitzHughNagumo oscillators. Front Phys 13:130503
Acknowledgments
The authors would like to thank Profs. N. Sarlis and D. Frantzeskakis for helpful discussions and scientific exchanges. NDTD acknowledges financial support from Greece and the European Union (European Social Fund - ESF) through the Operational Program “Human Resources Development, Education and Lifelong Learning” in the context of the project “Strengthening Human Resources Research Potential via Doctorate Research” (MIS-5000432), implemented by the State Scholarships Foundation (IKY). This work was supported by computational time granted by the Greek Research and Technology Network (GRNET) in the National HPC Facility – ARIS – under project CoBrain3 (ID PR005014).
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Tsigkri-DeSmedt, ND., Vlamos, P., Provata, A. (2020). Finite Size Effects in Networks of Coupled Neurons. In: Vlamos, P. (eds) GeNeDis 2018. Advances in Experimental Medicine and Biology, vol 1194. Springer, Cham. https://doi.org/10.1007/978-3-030-32622-7_37
Download citation
DOI: https://doi.org/10.1007/978-3-030-32622-7_37
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32621-0
Online ISBN: 978-3-030-32622-7
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)