The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry

Fang, Cheng; Li, Ji

doi:10.3934/math.2023171

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…The lower dimensional reduction (10) can be advantageous for analytical manipulations (c.f. [12]). In Fig.…”

Section: Results For Neural Spikementioning

confidence: 99%

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Golden Ratio Information for Neural Spike Code

Deng

2023

Preprint

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Spike bursting is a ubiquitous feature of all neuronal systems. Assuming the spiking states form an alphabet for a communication system, what is the optimal information precessing rate? and what is the channel capacity? Here we demonstrate that the quaternary alphabet of spike number code gives the maximal processing rate, and that a binary source in Golden Ratio distribution gives rise to the channel capacity. A multi-time scaled neural circuit is shown to satisfy the hypotheses of this neural communication system.

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“…The lower dimensional reduction (10) can be advantageous for analytical manipulations (c.f. [12]). In Fig.…”

Section: Results For Neural Spikementioning

confidence: 99%

“…Equation (12) for α gives a way to quantify how close something is to the Golden Ratio. For example, a rectangular frame is uniquely defined by its height-to-width (aspect) ratio.…”

Section: Results For Neural Spikementioning

confidence: 99%

Golden Ratio Information for Neural Spike Code

Deng

2023

Preprint

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Analysis for the hierarchical architecture of the heterogeneous FitzHugh-Nagumo network inducing synchronization

Yang

Park

2023

MATH

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<abstract><p>Synchronization is a key topic of research in neuroscience, medicine, and artificial neural networks; however, understanding its principle is difficult, both scientifically and mathematically. Specifically, the synchronization of the FitzHugh-Nagumo network with a hierarchical architecture has previously been studied; however, a mathematical analysis has not been conducted, owing to the network complexity. Therefore, in this paper, we saught to understand synchronization through mathematical analyses. In particular, we consider the most common types of hierarchical architecture and present a condition of the hierarchical architecture to induce synchronization. First, we provide mathematical analyses of a Lyapunov function for each layer, from which we obtain sufficient conditions guaranteeing synchronization and show that the Lyapunov function decreases exponentially. Moreover, we show that the internal connectivity critically affects synchronization in the first layer; however, in the second and subsequent layers, the internal connectivity is not important for synchronization, and the connectivity up to the first layer critically affects synchronization. We expect that the results and mathematical methodology can be applied to study other similar neural models with hierarchical architectures.</p></abstract>

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The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry

Cited by 2 publications

References 22 publications

Golden Ratio Information for Neural Spike Code

Golden Ratio Information for Neural Spike Code

Analysis for the hierarchical architecture of the heterogeneous FitzHugh-Nagumo network inducing synchronization

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