Effect of network structural perturbations on spiral wave patterns

Wang, Yafeng; Song, Dongmei; Gao, Xiang; Qu, Shi Xian; Lai, Ying–Cheng; Wang, Xingang

doi:10.1007/s11071-018-4283-1

Cited by 11 publications

(2 citation statements)

References 47 publications

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“…The advent of irregular patterns in electrically coupled networks are studied in horde of literatures [6,7,10,11,15,16,28,33,34] but many not considered the presence of obstacles and very few discussed influences of the obstacle size and orientation [35][36][37][38][39][40][41][42][43]. Even those are not considered multilayer networking strategy.…”

Section: Introductionmentioning

confidence: 99%

A Discrete Huber-braun Neuron Model: From Nodal Properties to Network Performance

Rajagopal²,

Karthikeyan

et al. 2021

Preprint

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Many of the well-known neuron models are continuous time systems with complex mathematical definitions. Literatures have shown that a discrete mathematical model can effectively replicate the complete dynamical behaviour of a neuron with much reduced complexity. Hence, we propose a new discrete neuron model derived from the Huber-Braun neuron with two additional slow and subthreshold currents alongside the ion channel currents. We have also introduced temperature dependent ion channels to study its effects on the firing pattern of the neuron. With bifurcation and Lyapunov exponents we showed the chaotic and periodic regions of the discrete model. Further to study the complexity of the neuron model, we have used the sample entropy algorithm. Though the individual neuron analysis gives us an idea about the dynamical properties, it’s the collective behaviour which decides the overall behavioural pattern of the neuron. Hence, we investigate the spatiotemporal behaviour of the discrete neuron model in single- and two-layer network. We have considered noise and obstacles as the two important factor which changes the excitability of the neurons in the network. When there is no noise or obstacle, the network display simple wave propagation with highly excitable neurons. Literatures have shown that spiral waves can play a positive role in breaking through quiescent areas of the brain as a pacemaker by creating a coherence resonance behaviour. Hence, we are interested in studying the induced spiral waves in the network. In this condition when an obstacle is introduced the wave propagation is disturbed and we could see multiple wave re-entry and spiral waves. Now when we consider only noise with no obstacle, for selected noise variances the network supports wave re-entry. By introducing an obstacle in this noisy network, the re-entry soon disappears, and the network soon enters idle state with no resetting. In a two-layer network when the obstacle is considered only in one layer and stimulus applied to the layer having the obstacle, the wave re-entry is seen in both the layer though the other layer is not exposed to obstacle. But when both the layers are inserted with an obstacle and stimuli also applied to the layers, they behave like independent layers with no coupling effect. This in a two-layer network stimulus play an important role in spatiotemporal dynamics of the network. Similar noise effects like the single layer network are also seen in the two-layer network.

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Section: Introductionmentioning

confidence: 99%

A Discrete Huber-braun Neuron Model: From Nodal Properties to Network Performance

Rajagopal²,

Karthikeyan

et al. 2021

Preprint

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“…In 1997, Spiral waves are captured experimentally in neuron system while investigating turtle visual cortex [39]. Multitude of theoretical models were developed to study the spiral wave formation [35,[40][41][42][43][44] and its dynamics [45][46][47][48][49][50], considerable literatures found in control scheme [48,[51][52][53][54][55][56].Periodic excitation of local neuron could be a potential method but recent literatures conceived few more methods to control or suppress spiral waves [48,51,[53][54][55][57][58][59]. Introduction of channel noise and additive noise found promising method to disintegrate the spiral waves smoothly [38,[60][61][62][63][64][65][66].…”

mentioning

confidence: 99%

Noise induced suppression of spiral waves in a hybrid FitzHugh–Nagumo neuron with discontinuous resetting

Rajagopal¹,

Jafari

Moroz

et al. 2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A modified FitzHugh-Nagumo neuron model with sigmoid function-based recovery variable is considered with electromagnetic flux coupling. The dynamical properties of the proposed neuron model are investigated and as the excitation current becomes larger, the number of fixed points decreases to one. The bifurcation plots are investigated to show the chaotic and periodic regimes for various values of excitation current and parameters. A network of the neuron model is constructed to study the wave propagation and wave re-entry phenomenon. Investigations are conducted to show that for larger flux coupling values, the spiral waves are suppressed but for such values of the flux coupling the individual nodes are driven into periodic regimes. By introducing Gaussian noise as an additional current term we showed that when noise is introduced for entire simulation time, the dynamics of the nodes are largely altered while the noise exposure for 200-time units will not alter the dynamics of the nodes completely. Keyboards: FitzHugh-Nagumo neuron; hybrid neuron; resetting; spiral waves; noise effectsFitzHugh-Nagumo neuron models are simplest yet one of the effective mathematical models used to define the bursting and spiking phenomenon of neurons. We modified the model by including sigmoid based recovery variable and flux coupling. Dynamical behaviours and properties of the modified model is investigated. A network model of the neuron model is constructed, and wave propagation phenomenon is studied. We could effectively show the emergence of spiral waves in the network and by including the noise effects we could show that introducing noise can suppress spiral waves.

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Improving the robustness of spatial networks by link addition: more and dispersed links perform better

et al. 2020

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Effect of network structural perturbations on spiral wave patterns

Cited by 11 publications

References 47 publications

A Discrete Huber-braun Neuron Model: From Nodal Properties to Network Performance

A Discrete Huber-braun Neuron Model: From Nodal Properties to Network Performance

Noise induced suppression of spiral waves in a hybrid FitzHugh–Nagumo neuron with discontinuous resetting

Improving the robustness of spatial networks by link addition: more and dispersed links perform better

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