Snakes and ladders in an inhomogeneous neural field model

PHYSICA D-NONLINEAR PHENOMENA

卷:294

Article

Avitabile, Daniele¹  Schmidt, Helmut² 

[1] Univ Nottingham, Ctr Math Med & Biol, Sch Math Sci, Nottingham NG7 2RD, England

[2] Univ Exeter, Coll Engn Math & Phys Sci, Exeter EX4 4QJ, Devon, England

关键词: Neural fields;    Bumps;    Localized states;    Snakes and ladders;    Inhomogeneities;   

DOI  :  10.1016/j.physd.2014.11.007

来源: Elsevier

【 摘 要 】

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 approach proposed by Beck and co-workers to analyze snaking solutions to the Swift-Hohenberg equation remains 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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free