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Snakes and ladders in an inhomogeneous neural field model (2014)
Journal Article
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

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... Read More about Snakes and ladders in an inhomogeneous neural field model.

Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in (2014)
Journal Article
Avitabile, D., Hoyle, R., & Samaey, G. (2014). Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in. SIAM Journal on Applied Dynamical Systems, 13(4), 1583-1619. https://doi.org/10.1137/140962188

We investigate the occurrence of coarse macroscopic states in an agent-based model of consumer lock-in. The system studied here is a modification of an existing model by Garlic and Chli [24] and it serves as a prototypical Ising-type sociological sys... Read More about Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in.

Spots: breathing, drifting and scattering in a neural field model (2014)
Book Chapter
Coombes, S., Schmidt, H., & Avitabile, D. (2014). Spots: breathing, drifting and scattering in a neural field model. In S. Coombs, P. Beim Graben, R. Potthast, & J. Wright (Eds.), Neural fields: theory and applications (187-211). Springer. https://doi.org/10.1007/978-3-642-54593-1_7

Two dimensional neural field models with short range excitation and long range inhibition can exhibit localised solutions in the form of spots. Moreover, with the inclusion of a spike frequency adaptation current, these models can also support breath... Read More about Spots: breathing, drifting and scattering in a neural field model.

Localised auxin peaks in concentration-based transport models for plants (2014)
Journal Article
Draelants, D., Avitabile, D., & Vanroose, W. Localised auxin peaks in concentration-based transport models for plants. Manuscript submitted for publication

We study the existence and bifurcation structure of stationary localised auxin spots in concentration-based auxin-transport models posed on one- and two-dimensional networks of plant cells. In regular domains with small active transport coefficient a... Read More about Localised auxin peaks in concentration-based transport models for plants.

Continuation of localised coherent structures in nonlocal neural field equations (2014)
Journal Article
Rankin, J., Avitabile, D., Baladron, J., Faye, G., & Lloyd, D. J. (2014). Continuation of localised coherent structures in nonlocal neural field equations. SIAM Journal on Scientific Computing, 36(1), Article B70-B93. https://doi.org/10.1137/130918721

We study localised activity patterns in neural field equations posed on the Euclidean plane; such models are commonly used to describe the coarse-grained activity of large ensembles of cortical neurons in a spatially continuous way. We employ matrix-... Read More about Continuation of localised coherent structures in nonlocal neural field equations.