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Snakes and ladders in an inhomogeneous neural field model

Avitabile, Daniele; Schmidt, Helmut

Authors

Daniele Avitabile Daniele.Avitabile@nottingham.ac.uk

Helmut Schmidt pmxhs@nottingham.ac.uk



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.

Journal Article Type Article
Publication Date Feb 15, 2015
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Peer Reviewed Not Peer Reviewed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
APA6 Citation Avitabile, D., & Schmidt, H. (2015). Snakes and ladders in an inhomogeneous neural field model. Physica D: Nonlinear Phenomena, 294, 24-36. doi:10.1016/j.physd.2014.11.007
DOI https://doi.org/10.1016/j.physd.2014.11.007
Publisher URL https://www.sciencedirect.com/science/article/pii/S0167278914002280
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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