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Complete dynamical analysis of a neocortical network model

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Abstract

The brain is a complex system consisting of a large number of interacting neurons. Recently, a simple nonlinear biological model has been proposed for the up and down state transitions in the network of excitatory and inhibitory neurons. In this paper, we study the dynamical behavior of this model by calculating the Lyapunov exponents and bifurcation diagrams for various values of synaptic connections. We show that varying the synaptic strength values has a considerable effect on the bifurcations in the model. Furthermore, we show that the model can exhibit chaotic firing for certain values of the excitatory–excitatory synaptic strength.

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Acknowledgements

Matjaž Perc was supported by the Slovenian Research Agency (Grant Nos. J4-9302, J1-9112, and P1-0403).

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Authors and Affiliations

  1. Neural Engineering Laboratory, Department of Biomedical Engineering, University of Neyshabur, Neyshabur, Iran

    Ali Foroutannia & Mahdieh Ghasemi

  2. Department of Biomedical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran, 15875-4413, Iran

    Fatemeh Parastesh & Sajad Jafari

  3. Health Technology Research Institute, Amirkabir University of Technology, 424 Hafez Ave., Tehran, 15875-4413, Iran

    Sajad Jafari

  4. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia

    Matjaž Perc

  5. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Matjaž Perc

  6. Complexity Science Hub Vienna, Josefstädterstraße 39, 1080, Vienna, Austria

    Matjaž Perc

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  1. Ali Foroutannia
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Correspondence to Matjaž Perc.

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Foroutannia, A., Ghasemi, M., Parastesh, F. et al. Complete dynamical analysis of a neocortical network model. Nonlinear Dyn 100, 2699–2714 (2020). https://doi.org/10.1007/s11071-020-05668-6

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  • DOI: https://doi.org/10.1007/s11071-020-05668-6

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