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

Axel Hutt 1 Linghai Zhang 2
1 NEUROSYS - Analysis and modeling of neural systems by a system neuroscience approach
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
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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Axel Hutt, Linghai Zhang. Distributed nonlocal feedback delays may destabilize fronts in neural fields, distributed transmission delays do not. Journal of Mathematical Neuroscience, BioMed Central, 2013. ⟨hal-00847168⟩

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