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 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.
Original language | English |
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Pages (from-to) | 24-36 |
Number of pages | 13 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 294 |
DOIs | |
Publication status | Published - 15 Feb 2015 |
Externally published | Yes |
Keywords
- Bumps
- Inhomogeneities
- Localized states
- Neural fields
- Snakes and ladders