Synchronizability of two neurons with switching in the coupling

Parastesh, Fatemeh; Azarnoush, Hamed; Jafari, Sajad; Hatef, Boshra; Perc, Matjaž; Repnik, Robert

doi:10.1016/j.amc.2019.01.011

Cited by 65 publications

(22 citation statements)

References 36 publications

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“…If the state variables of two coupled systems have the same amplitude but different signs, the form of synchronization is called anti-phase synchronization. To quantitatively depict the error of two coupled neural networks, a normalized mean synchronization error e m can be defined as [45]:…”

Section: B Numerical Validationsmentioning

confidence: 99%

“…Indeed, during the past few decades, many investigations have been devoted to achieving the synchronization of neural networks by using various control approaches [37][38][39][40][41]. There are also some works investigating the phenomenon of firing synchronization in coupled bineuron networks in recent years [42][43][44][45]. For example, in [46], bursting synchronization of two coupled ML neurons under electromagnetic radiation was studied.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Neural Bursting and Synchronization Emulated by Neural Networks and Circuits

Lin

Wang

Chen

et al. 2021

IEEE Trans. Circuits Syst. I

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Nowadays, research, modeling, simulation and realization of brain-like systems to reproduce brain behaviors have become urgent requirements. In this paper, neural bursting and synchronization are imitated by modeling two neural network models based on the Hopfield neural network (HNN). The first neural network model consists of four neurons, which correspond to realizing neural bursting firings. Theoretical analysis and numerical simulation show that the simple neural network can generate abundant bursting dynamics including multiple periodic bursting firings with different spikes per burst, multiple coexisting bursting firings, as well as multiple chaotic bursting firings with different amplitudes. The second neural network model simulates neural synchronization using a coupling neural network composed of two above small neural networks. The synchronization dynamics of the coupling neural network is theoretically proved based on the Lyapunov stability theory. Extensive simulation results show that the coupling neural network can produce different types of synchronous behaviors dependent on synaptic coupling strength, such as anti-phase bursting synchronization, anti-phase spiking synchronization, and complete bursting synchronization. Finally, two neural network circuits are designed and implemented to show the effectiveness and potential of the constructed neural networks.

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Section: B Numerical Validationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Neural Bursting and Synchronization Emulated by Neural Networks and Circuits

Lin

Wang

Chen

et al. 2021

IEEE Trans. Circuits Syst. I

View full text Add to dashboard Cite

show abstract

“…For the synchronization behaviors of two coupled neurons and neuronal network, a lot of researches have been done by relevant scholars . For the synchronization behaviors of two coupled neurons, the synchronization transition [5,6] and the influence of different coupling way [7][8][9] are investigated. The synchronization transition of two coupled ML neurons is studied in [5], and it found that the bursting synchronization happens before spiking synchronization.…”

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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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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“…Recently, the effect of electromagnetic field has been investigated on the collective behavior of neurons [13][14][15]. Thus the analysis of synchronization of neuronal networks is an important research area and has attracted considerable attention [16][17][18][19][20][21]. These studies are often considered as efficient mechanisms in identifying neural disorders such as Parkinson [22].…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior and network analysis of an extended Hindmarsh–Rose neuron model

et al. 2019

Self Cite

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In this paper, the extended Hindmarsh-Rose neuron model, which considers the slow intracellular exchange of calcium ions between its store and the cytoplasm, is studied. The dynamical behavior of this neuron model is analyzed by deriving the equilibrium points, the bifurcation diagrams, and the Lyapunov exponents, in the presence of an external forcing current. Furthermore, the dynamics of the network of the extended model is investigated. Firstly, a one-dimensional ring network is constructed, and the effects of the coupling strength and the forcing current are considered on the network behavior. The results confirm the existence of chimera state in small coupling strength values. Then a square network of the proposed model is created by adding an external excitation to the neurons

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Synchronizability of two neurons with switching in the coupling

Cited by 65 publications

References 36 publications

Neural Bursting and Synchronization Emulated by Neural Networks and Circuits

Neural Bursting and Synchronization Emulated by Neural Networks and Circuits

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

Dynamical behavior and network analysis of an extended Hindmarsh–Rose neuron model

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