Investigating bifurcation points of neural networks: application to the epileptic seizure
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Investigating bifurcation points of neural networks: application to the epileptic seizure Zahra Faghani 1 , Sajad Jafari 2,3 , Chao-Yang Chen 4,5 , and Fahimeh Nazarimehr 2,a 1 2 3
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Bernstein Center for Computational Neuroscience Berlin, Philippstr. 13, Haus 6, 10115 Berlin, Germany Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran Health Technology Research Institute, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, P.R. China Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA Received 10 September 2020 / Received in final form 27 September 2020 / Accepted 1 October 2020 Published online 2 December 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. In this paper, we investigate epileptic seizures with the help of bifurcations in the network of neurons. The bifurcations of these neurons are investigated in one-layer and multi-layer network with different coupling strength. Bifurcations of networks are studied in various aspects. Also, dynamical properties of different networks and the single neuron out of network are compared. Some measures are reviewed to predict the bifurcation points of a network. These measures are justified by the bifurcations’ plots. The main goal of this paper is investigating the bifurcations in networks of neurons and studying their dynamical properties. Also, the results are discussed from the viewpoint of physiological facts.
1 Introduction Neurons are considered as the fundamental unit of the neural system [1,2]. Neurons’ electrical activities exhibit strong non-linear properties [3]. Some neuron models could mimic these electrical activities and help us to understand real neurons better. Models of neurons such as Hodgkin-Huxley [4] and Moris-Lecar [5] have demonstrated the influence of ion channels on membrane potential. Ibarz et al. [6] have studied the map-type neuron model which could be useful to generate the dynamical properties in neuronal activities. Also, the three-variable Hindmarsh-Rose neuron model (HR) [7] which is one of the developed versions of the Hodgkin-Huxley model could show the neuronal activities’ feature and bifurcations [8,9]. One of the modified version of the HR model is a four variable HR neuron model which could describe a large variety of neuronal activities and exhibit chaos in a broad range of parameters [10,11]. This model also was confirmed by experimental results [12]. The neural system is comprised of a large number of neurons. The Complex behavior of neurons have been studied for many years [13–16]. Researchers believe that the studying of neuronal models and neuronal networks are beneficial to define some neuronal system diseases [17]. Coupling neurons have been investigated man
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