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Rapport (Rapport De Recherche) Année : 2012

Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis

Résumé

The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.
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Dates et versions

hal-00665464 , version 1 (02-02-2012)

Identifiants

  • HAL Id : hal-00665464 , version 1

Citer

Grégory Faye, James Rankin, Pascal Chossat. Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis. [Research Report] RR-7872, INRIA. 2012, pp.31. ⟨hal-00665464⟩
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