title: Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis.
abstract: 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.
authors.affiliation: NeuroMathComp Laboratory, INRIA, ENS Paris, 2004 Route des Lucioles, BP 93, 06902, Sophia-Antipolis, France. gregory.faye@inria.fr
authors.forename: Grégory
authors.initials: G
authors.lastname: Faye
authors.forename: James
authors.initials: J
authors.lastname: Rankin
authors.forename: Pascal
authors.initials: P
authors.lastname: Chossat
mesh_terms: D000200:Action Potentials / Q000502:physiology; D055641:Mathematical Concepts; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*