Distributed nonlocal feedback delays may destabilize fronts in neural fields, distributed transmission delays do not - Archive ouverte HAL Access content directly
Journal Articles Journal of Mathematical Neuroscience Year : 2013

Distributed nonlocal feedback delays may destabilize fronts in neural fields, distributed transmission delays do not

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Abstract

The spread of activity in neural populations is a well-known phenomenon. To understand the propagation speed and the stability of stationary fronts in neural populations, the present work considers a neural field model that in- volves intra-cortical and cortico-cortical synaptic interactions. This includes distributions of axonal transmission speeds and nonlocal feedback delays as well as general classes of synaptic interactions. The work proves the spec- tral stability of standing and travelling fronts subject to general transmission speeds for large classes of spatial interactions and derives conditions for the front instabilities subjected to nonlocal feedback delays. Moreover it turns out that the uniqueness of the stationary travelling fronts guarantees its exponential stability for vanishing feedback delay. Numerical simulations complement the analytical findings.
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Dates and versions

hal-00847168 , version 1 (22-07-2013)

Identifiers

  • HAL Id : hal-00847168 , version 1

Cite

Axel Hutt, Linghai Zhang. Distributed nonlocal feedback delays may destabilize fronts in neural fields, distributed transmission delays do not. Journal of Mathematical Neuroscience, 2013. ⟨hal-00847168⟩
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