Propagation of firing rate by synchronization in a feed-forward multilayer Hindmarsh–Rose neural network

Ge, Mengyan; Jia, Ya; Kirunda, John Billy; Xu, Ying; Shen, Ju; Liu, Lulu; Liu, Ying; Pei, Qiuming; Zhan, Xuan; Yang, Lijian

doi:10.1016/j.neucom.2018.09.037

Cited by 60 publications

(15 citation statements)

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“…This paper investigates the synchronization behavior and synchronization transition in three cases, which are the fractional-order HR model's ring neuronal network without electromagnetic radiation, two coupled fractional-order neuronal models under electromagnetic radiation and fractional-order ring neuronal network under electromagnetic radiation. First, for the fractionalorder model's ring neuronal network without electromagnetic radiation, like other influence factors reported in [21][22][23][24][25][26][27][28][29][30][31][32][33], the fractional-order can also change the threshold of the coupling strength. And the transition of periodic synchronization and chaotic synchronization induced by the fractional-order is found.…”

Section: Discussionmentioning

confidence: 99%

“…When multiple neurons are coupled into a network, there will be more emergence phenomenon. Many researchers investigated the factors influencing network synchronization [10][11][12][13][14][15][16][17][18][19][20][21][22][23], such as the network topology [10][11][12][13][14], the time delay and partial time delay [15,16], the coupled way and initial value [17][18][19][20], and the layers of networks [21]. In the previous researches, most neuron models are integer-order models.…”

Section: Introductionmentioning

confidence: 99%

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The Synchronization and Synchronization Transition of Coupled Fractional-order Neuronal Networks

Xin

Zhang

et al. 2021

Preprint

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Different from the previous researches on the synchronization and synchronization transition of neuronal networks constructed by integer-order neuronal models, the synchronization and synchronization transition of fractional-order neuronal network are investigated in this paper. The fractional-order ring neuronal network constructed by fractional-order HindmarshRose (HR) neuronal models without electromagnetic radiation are proposed, and it’s synchronization behaviors are investigated numerically. The synchronization behaviors of two coupled fractional-order neuronal models and ring neuronal network under electromagnetic radiation are studied numerically. By research results, several novel phenomena and conclusions can be drawn. First, for the fractional-order HR model’s ring neuronal network without electromagnetic radiation, if the fractional-order q is changed, the threshold of the coupling strength when the network is in perfect synchronization will change. Furthermore, the change of fractional-order can induce the transition of periodic synchronization and chaotic synchronization. Second, for the two coupled neurons under electromagnetic radiation, the synchronization degree is influenced by fractional-order and the feedback gain parameter k1 . In addition, the fractional-order and parameter k1 can induce the synchronization transition of bursting synchronization, perfect synchronization and phase synchronization. For the perfect synchronization, the synchronization transition of chaotic synchronization and periodic synchronization induced by q and parameter k1 is also observed. Especially, When the fractionalorder is small, like 0.6, the synchronization behavior will be more complex. Third, for the ring neuronal network under electromagnetic radiation, with the change of memory-conductance parameter β, parameter k1 and fractional-order q of electromagnetic radiation, the synchronization behaviors are different. When β > 0.02 , the synchronization will be strengthened with the decreasing of fractional-order. The parameter k1 can induce the synchronization transition of perfect periodic10 synchronization, perfect periodic-7 synchronization, perfect periodic-5 synchronization and perfect periodic4 synchronization. It is hard for the system to synchronize and q has little effect on the synchronization when −0.06 < β < 0.02 . When β < −0.06 , the network moves directly from asynchronization to perfect synchronization, and the synchronization factor goes from 0.1 to 1 with the small change of fractional-order. Larger the factional-order is, larger the range of synchronization is. The synchronization degree increases with the increasing of k1.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Synchronization and Synchronization Transition of Coupled Fractional-order Neuronal Networks

Xin

Zhang

et al. 2021

Preprint

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“…It is all known that abundant collective behaviors appear in the actual neural system due to the interactions in neurons [153,154]; among them, synchronization is the outstanding collective features in neuroscience [155][156][157], which is regarded as one of the mechanisms to propagate and to code information in brain [158,159]. However, there are different kinds of brain disorder diseases, such as Alzheimer's, epilepsy, Parkinson's, and schizophrenia, which are involved with the abnormal activities of synchronization [160].…”

Section: Synchronization Application Of Memristor-coupled Systemmentioning

confidence: 99%

Recent Advances in Dimensionality Reduction Modeling and Multistability Reconstitution of Memristive Circuit

2021

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Due to the introduction of memristors, the memristor-based nonlinear oscillator circuits readily present the state initial-dependent multistability (or extreme multistability), i.e., coexisting multiple attractors (or coexisting infinitely many attractors). The dimensionality reduction modeling for a memristive circuit is carried out to realize accurate prediction, quantitative analysis, and physical control of its multistability, which has become one of the hottest research topics in the field of information science. Based on these considerations, this paper briefly reviews the specific multistability phenomenon generating from the memristive circuit in the voltage-current domain and expounds the multistability control strategy. Then, this paper introduces the accurate flux-charge constitutive relation of memristors. Afterwards, the dimensionality reduction modeling method of the memristive circuits, i.e., the incremental flux-charge analysis method, is emphatically introduced, whose core idea is to implement the explicit expressions of the initial conditions in the flux-charge model and to discuss the feasibility and effectiveness of the multistability reconstitution of the memristive circuits using their flux-charge models. Furthermore, the incremental integral transformation method for modeling of the memristive system is reviewed by following the idea of the incremental flux-charge analysis method. The theory and application promotion of the dimensionality reduction modeling and multistability reconstitution are proceeded, and the application prospect is prospected by taking the synchronization application of the memristor-coupled system as an example.

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“…Content may change prior to final publication. networks [4][5][6][7][8][9][10][11][12][13][14][15]. The relevant literature shows that the main factors affecting the synchronization of coupled neuronal networks are the network topology [4][5][6][7][8], time delay in the network [9,10], coupling strength [11][12][13][14], and multilayer network structure [15], etc.…”

Section: Introductionmentioning

confidence: 99%

“…networks [4][5][6][7][8][9][10][11][12][13][14][15]. The relevant literature shows that the main factors affecting the synchronization of coupled neuronal networks are the network topology [4][5][6][7][8], time delay in the network [9,10], coupling strength [11][12][13][14], and multilayer network structure [15], etc. Recently, researchers have found that the electrical activity of neurons may be affected by electromagnetic fields, and thus, electromagnetic fields can be detected by the neuronal system [16,17].…”

Section: Introductionmentioning

confidence: 99%

The Synchronization Behaviors of Memristive Synapse-Coupled Fractional-Order Neuronal Networks

Yang

Zhang

2021

IEEE Access

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The synchronization behaviors of memristive synapse-coupled fractional-order neuronal networks are investigated in this paper. Based on the integer-order memristive synapse-coupled neuronal network, a fractional-order model is proposed, and a ring network composed of fractional-order memristive synapse-coupled neuronal subnetworks is constructed. Then, the synchronization behaviors of two fractional-order memristive synapse-coupled neurons and the ring fractional-order memristive synapsecoupled neuronal network are discussed numerically. These research results suggest several novel phenomena and allow several conclusions to be drawn. For the two coupled neurons, different fractionalorders can change the threshold of memristive synapse parameter 1 k when the two neurons are in perfect synchronization. The synchronization transitions are affected by the fractional-order and memristive synapse. Different from the integer-order model, perfect synchronization can occur before phase synchronization for some fractional-orders. Under a certain external current intensity, the transition between periodic synchronization and chaotic synchronization occurs as the fractional-order changes. The chaotic synchronization range is larger because of the memristive synapse. For the ring neuronal network coupled subnetworks, the results illustrate that the collective behaviors including incoherent, coherent, and chimera states can be induced by the fractional-order. In addition, the network's synchronization degree is influenced by the fractional-order. The synchronization transition of the neuronal network also occurs with changes in the fractional-order.

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Propagation of firing rate by synchronization in a feed-forward multilayer Hindmarsh–Rose neural network

Cited by 60 publications

References 64 publications

The Synchronization and Synchronization Transition of Coupled Fractional-order Neuronal Networks

The Synchronization and Synchronization Transition of Coupled Fractional-order Neuronal Networks

Recent Advances in Dimensionality Reduction Modeling and Multistability Reconstitution of Memristive Circuit

The Synchronization Behaviors of Memristive Synapse-Coupled Fractional-Order Neuronal Networks

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