Synchronization transitions induced by partial time delay in a excitatory–inhibitory coupled neuronal network

Sun, Xiaojuan; Guo-Fang, Li

doi:10.1007/s11071-017-3600-4

Cited by 51 publications

(17 citation statements)

References 54 publications

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“…In addition, the PIR spike or spiking are paradoxical phenomenon induced by inhibitory stimulations. Considering that the novel condition for PIR spike or spiking and multiple paradoxical phenomena induced by inhibitory effect [30] are helpful for identification of novel functions of inhibitory modulations in the nervous system [27], the relationship between paradoxical phenomenon such as the PIR spike and more kinds of bifurcations should be identified in future.…”

Section: 34mentioning

confidence: 99%

Big homoclinic orbit bifurcation underlying post-inhibitory rebound spike and a novel threshold curve of a neuron

Wang

2021

era

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Post-inhibitory rebound (PIR) spike induced by the negative stimulation, which plays important roles and presents counterintuitive nonlinear phenomenon in the nervous system, is mainly related to the Hopf bifurcation and hyperpolarization-active caution (I h) current. In the present paper, the emerging condition for the PIR spike is extended to the bifurcation of the big homoclinic (BHom) orbit in a model without I h current. The threshold curve for a spike evoked from a mono-stable or coexisting steady state surrounds the steady state from left, to below, and to right, because the BHom orbit is big enough to surround the steady state. The right part of the threshold curve coincides with the stable manifold of the saddle and acts the threshold for the spike induced by the positive stimulation, resembling that of the saddle-node bifurcation on an invariant cycle, and the left part acts the threshold for the PIR spike, resembling that of the Hopf bifurcation. The bifurcation curve and a codimension-2 bifurcation point related to the BHom orbit are acquired in the two-parameter plane. The results present a comprehensive viewpoint to the dynamics near the BHom orbit bifurcation, which presents a novel threshold curve and extends the conditions for the PIR spike.

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Section: 34mentioning

confidence: 99%

Big homoclinic orbit bifurcation underlying post-inhibitory rebound spike and a novel threshold curve of a neuron

Wang

2021

era

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“…When the number of network N is large enough and the rewiring probability p is sufficiently small, the properties of the NW model are quite similar to those of the WS model. Recent studies about the neuronal system are also under the NW small-world networks [18], [44]. Hence, in our simulation, we use the Newman-Watts (NW) small-world structure.…”

Section: B Network Structurementioning

confidence: 99%

Synchronization and Rhythm Transition in a Complex Neuronal Network

et al. 2020

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Synchronization and rhythm transition in an excitatory-inhibitory balanced cortical neuronal network are investigated in this paper. A small-world neuronal network is performed to be the cortical region of cerebral cortex, which is composed of different types of Izhikevich neurons. The combination of regular spiking (RS) cells, chattering (CH) cells, or mixed RS and CH cells are imitated as excitatory neurons, whereas fast spiking (FS) cells mimic inhibitory neurons. We mainly focus on the effect of different types of neurons on synchronization and rhythm transition of the neuronal network. The simulation results illustrate that it is easier for the neuronal network with CH excitatory neurons to achieve synchronization, and it is also more susceptible to the parameters than the network with RS neurons. Together with the weight of the synaptic connection, the structure of the small-world network is also explored to identify its influence on the synchronization and the rhythm transition. Moreover, we found that the synchronization performance could be improved by increasing the degree of influence among neurons. Importantly, the synchronization states are associated with the rhythm transitions. Especially, the consistency of synchronization of the neuronal network and γ band rhythm is illustrated. In addition, our results could have an important significance on further understanding brain rhythms and synchrony in neuroscience.

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“…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%

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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Synchronization transitions induced by partial time delay in a excitatory–inhibitory coupled neuronal network

Cited by 51 publications

References 54 publications

Big homoclinic orbit bifurcation underlying post-inhibitory rebound spike and a novel threshold curve of a neuron

Big homoclinic orbit bifurcation underlying post-inhibitory rebound spike and a novel threshold curve of a neuron

Synchronization and Rhythm Transition in a Complex Neuronal Network

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

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