Cluster synchronization and firing rate oscillation induced by time delay in random network of adaptive exponential inte
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Cluster synchronization and firing rate oscillation induced by time delay in random network of adaptive exponential integrate-and-fire neural system Lulu Lu, Lijian Yang, Xuan Zhan, and Ya Jia a Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, P.R. China
Received 15 July 2020 / Received in final form 9 September 2020 / Accepted 17 September 2020 Published online 9 November 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. Both time delay and coupling form are the most important factors in neural networks. The properties of firing rate oscillation and cluster synchronization induced by time delay are studied in random network of different coupling neurons. In previous work, the firing rate oscillation of cortical network was observed at the presence of three factors (time delay, weak sinusoidal signal, and noise). Here, we found that the firing rate oscillation can be induced only by the time delay, and the spike train can be propagated at a certain interval time, which is consistent with the value of delay time. Furthermore, the phenomenon of cluster synchronization occurs in random network, which may originates from network structure, and this connection between the neurons trigger spikes within a time-restricted window, resulting in cluster synchronization between corresponding neurons. These numerical results provide a potential theoretical basis for certain pathological brain rhythms associated with epileptic seizures.
1 Introduction The synchronization means that two or more quantities maintain a certain relative relationship during the change, and neural synchronization is the adjustment of rhythms of oscillating systems due to neural interaction [1–3]. The synchronization and electrical pattern of neural network are of great significance in neuroscience [4]. Mode transition and phase synchronization were discussed with time delay and noise in coupled neuron [5], and the stability and bifurcation in two coupled excitable neurons were investigated [6]. The synchronization of delay-coupled network was discussed [7,8], and synchronization of two coupled networks can be achieved under time-varying delay. The transition of synchronization was discussed under electromagnetic radiation [9–11], and found that synchronization depends on the coupling intensity and electromagnetic radiation intensity. Synchronization and wave propagation can be caused by chemical autapse [12], and the propagation of firing rate was contemplated in feed-forward multilayer Hindmarsh–Rose neural network [13]. Furthermore, chimera states (both synchronous and asynchronous states coexist) in local delay-coupling units and neural network were studied [14,15], and it shown that the relevance of different types of chimera states. The neural system’s response to weak signal [16] is also significant, and how to enhance the transmission of weak signal, distinguish or extract
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