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Controlling the Chimera Form in the Leaky Integrate-and-Fire Model

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GeNeDis 2020

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 1338))

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Abstract

We study the influence of broken connectivity and frequency disorder in systems of coupled neuronal oscillators. Under nonlocal coupling, systems of nonlinear oscillators, such as Kuramoto, FitzHugh-Nagumo, or integrate-and-fire oscillators, demonstrate nontrivial synchronization patterns. One of these patterns is the “chimera state,” which consists of coexisting coherent and incoherent domains. In networks of biological neurons, the connectivity is not always perfect, but might be locally broken or interrupted due to pathologies, neuron degenerative disorders, or accidents. Our simulations show that destructed connectivity drastically affects synchronization, driving the coherent parts of the chimera state to cover symmetrically the region where the anomaly is located. The network synchronization decreases with the size of the destructed region as evidenced by the Kuramoto synchronization index. To the contrary, when keeping the connectivity of all nodes intact, altering the frequency in a block of oscillators drives the incoherent part of the chimera state toward the anomaly. This work is in line with recent dynamical approaches aiming to locate anomalies in the structure of brain networks, in particular when the anomalies have small, difficult-to-detect sizes.

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Acknowledgments

The authors would like to thank Dr. J. Hizanidis, Dr. N. D. Tsigkri-DeSmedt, and T. Kasimatis for fruitful discussions. A.P. and Ch.G.A. acknowledge the support provided by the London Mathematical Society (LMS) Research in Pairs Scheme 4, Grant No 41903. We acknowledge the partial support of this work by the project MIS 5002567, implemented under the “Action for the Strategic Development on the Research and Technological Sector,” funded by the “Operational Programme Competitiveness, Entrepreneurship and Innovation” (NSRF 2014–2020) and co-financed by Greece and the European Union (European Regional Development Fund). This work was supported by computational time granted by the Greek Research and Technology Network (GRNET) at the National HPC Facility – ARIS – under projects CoBrain4 (ID: PR007011) and CoBrain5 (ID: PR009012).

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Authors and Affiliations

  1. Institute of Nanoscience and Nanotechnology, National Center for Scientific Research “Demokritos”, Athens, Greece

    A. Provata

  2. Department of Mathematical Sciences, University of Essex, Wivenhoe Park, UK

    Ch. G. Antonopoulos

  3. Department of Informatics, Ionian University, Corfu, Greece

    P. Vlamos

Authors
  1. A. Provata
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  2. Ch. G. Antonopoulos
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  3. P. Vlamos
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Correspondence to A. Provata .

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Editors and Affiliations

  1. Department of Informatics, Ionian University, Corfu, Greece

    Panayiotis Vlamos

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Provata, A., Antonopoulos, C.G., Vlamos, P. (2021). Controlling the Chimera Form in the Leaky Integrate-and-Fire Model. In: Vlamos, P. (eds) GeNeDis 2020. Advances in Experimental Medicine and Biology, vol 1338. Springer, Cham. https://doi.org/10.1007/978-3-030-78775-2_30

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