We study the existence and stability of localized activity states in neuronal network models of feature selectivity with either a ring or spherical topology. We find that the neural field has mono-stable, bi-stable, and tri-stable regimes depending on the parameters of the weighting function. In the case of homogeneous inputs, these localized activity states are marginally stable with respect to rotations. The response of a stable equilibrium to an inhomogeneous input is also determined.
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