Daniele Avitabile
Snakes and ladders in an inhomogeneous neural field model
Avitabile, Daniele; Schmidt, Helmut
Authors
Helmut Schmidt
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.
Citation
Avitabile, D., & Schmidt, H. (2015). Snakes and ladders in an inhomogeneous neural field model. Physica D: Nonlinear Phenomena, 294, 24-36. https://doi.org/10.1016/j.physd.2014.11.007
Journal Article Type | Article |
---|---|
Acceptance Date | Nov 27, 2014 |
Online Publication Date | Dec 5, 2014 |
Publication Date | Feb 15, 2015 |
Deposit Date | Mar 17, 2014 |
Publicly Available Date | Dec 5, 2014 |
Journal | Physica D: Nonlinear Phenomena |
Print ISSN | 0167-2789 |
Electronic ISSN | 0167-2789 |
Publisher | Elsevier |
Peer Reviewed | Not Peer Reviewed |
Volume | 294 |
Pages | 24-36 |
DOI | https://doi.org/10.1016/j.physd.2014.11.007 |
Public URL | https://nottingham-repository.worktribe.com/output/997960 |
Publisher URL | https://www.sciencedirect.com/science/article/pii/S0167278914002280 |
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