Snakes and ladders in an inhomogeneous neural field model

Avitabile, Daniele and Schmidt, Helmut (2014) Snakes and ladders in an inhomogeneous neural field model. Physica D: Nonlinear Phenomena . ISSN 0167-2789 (Submitted)

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Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with

periodic modulation of the synaptic connectivity kernel and find that they are arranged in a snakes-and-ladders bifurcation structure. In the case of Heaviside firing rates, we construct analytically symmetric and asymmetric states and hence derive closed-form expressions for the corresponding bifurcation diagrams. We show that the ideas proposed by Beck and co-workers to analyze snaking solutions to the Swift--Hohenberg equation remain valid for the neural field model, even though the corresponding spatial-dynamical formulation is non-autonomous. We investigate how the modulation amplitude affects the bifurcation structure and compare numerical calculations for steep sigmoidal firing rates with analytic predictions valid in the Heaviside limit.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Depositing User: Avitabile, Dr. Daniele
Date Deposited: 17 Mar 2014 00:02
Last Modified: 04 May 2020 20:16

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