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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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Abstract

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
RIS ID:	https://nottingham-repository.worktribe.com/output/997960
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
URI:	https://eprints.nottingham.ac.uk/id/eprint/2328

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