Research Repository

See what's under the surface


Next-generation neural field model: The evolution of synchrony within patterns and waves (2019)
Journal Article
Byrne, Á., Avitabile, D., & Coombes, S. (2019). Next-generation neural field model: The evolution of synchrony within patterns and waves. Physical Review E, 99(1), doi:10.1103/physreve.99.012313

Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the neural tissue... Read More

Network mechanisms underlying the role of oscillations in cognitive tasks (2018)
Journal Article
Schmidt, H., Avitabile, D., Montbrió, E., & Roxin, A. (2018). Network mechanisms underlying the role of oscillations in cognitive tasks. PLoS Computational Biology, 14(9), 1-24. doi:10.1371/journal.pcbi.1006430

Oscillatory activity robustly correlates with task demands during many cognitive tasks. However, not only are the network mechanisms underlying the generation of these rhythms poorly understood, but it is also still unknown to what extent they may pl... Read More

Modal nudging in nonlinear elasticity: tailoring the elastic post-buckling behaviour of engineering structures (2018)
Journal Article
Cox, B., Groh, R., Avitabile, D., & Pirrera, A. (2018). Modal nudging in nonlinear elasticity: tailoring the elastic post-buckling behaviour of engineering structures. Journal of the Mechanics and Physics of Solids, 116, doi:10.1016/j.jmps.2018.03.025. ISSN 0022-5096

The buckling and post-buckling behaviour of slender structures is increasingly being harnessed for smart functionalities. Equally, the post-buckling regime of many traditional engineering structures is not being used for design and may therefore harb... Read More

Neural Fields: Localised States with Piece-Wise Constant Interactions (2018)
Book Chapter
Gökçe, A., Coombes, S., & Avitabile, D. (2018). Neural Fields: Localised States with Piece-Wise Constant Interactions. In Mathematical and Theoretical Neuroscience: Cell, Network and Data AnalysisSpringer Nature. doi:10.1007/978-3-319-68297-6_7

Neural field models are typically cast as continuum integro-differential equations for describing the idealised coarse-grained activity of populations of interacting neurons. For smooth Mexican hat kernels, with short-range excitation and long-range... Read More

Spot dynamics in a reaction-diffusion model of plant root hair initiation (2018)
Journal Article
Avitabile, D., Brena-Medina, V. F., & Ward, M. J. (2018). Spot dynamics in a reaction-diffusion model of plant root hair initiation. SIAM Journal on Applied Mathematics, 78(1), doi:10.1137/17M1120932. ISSN 0036-1399

We study pattern formation in a 2-D reaction-diffusion (RD) sub-cellular model characterizing the effect of a spatial gradient of a plant hormone distribution on a family of G-proteins associated with root-hair (RH) initiation in the plant cell Arabi... Read More

Synchrony-induced modes of oscillation of a neural field model (2017)
Journal Article
Esnaola-Acebes, J. M., Roxin, A., Avitabile, D., & Montbrio, E. (2017). Synchrony-induced modes of oscillation of a neural field model. Physical Review E, 96(5), doi:10.1103/PhysRevE.96.052407. ISSN 2470-0045

We investigate the modes of oscillation of heterogeneous ring-networks of quadratic integrate-and-fire (QIF) neurons with non-local, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient stan... Read More

The dynamics of neural fields on bounded domains: an interface approach for Dirichlet boundary conditions (2017)
Journal Article
Gökçe, A., Avitabile, D., & Coombes, S. (in press). The dynamics of neural fields on bounded domains: an interface approach for Dirichlet boundary conditions. Journal of Mathematical Neuroscience, 7, doi:10.1186/s13408-017-0054-4. ISSN 2190-8567

Continuum neural field equations model the large scale spatio-temporal dynamics of interacting neurons on a cortical surface. They have been extensively studied, both analytically and numerically, on bounded as well as unbounded domains. Neural field... Read More

Spatio-temporal canards in neural field equations (2017)
Journal Article
Avitabile, D., Desroches, M., & Knobloch, E. (in press). Spatio-temporal canards in neural field equations. Physical Review E, 95(4), doi:10.1103/PhysRevE.95.042205. ISSN 2470-0045

Canards are special solutions to ordinary differential equations that follow invariant repelling slow manifolds for long time intervals. In realistic biophysical single-cell models, canards are responsible for several complex neural rhythms observed... Read More

Beyond in-phase and anti-phase coordination in a model of joint action (2016)
Journal Article
Avitabile, D., Słowiński, P., Bardy, B., & Tsaneva-Atanasova, K. (in press). Beyond in-phase and anti-phase coordination in a model of joint action. Biological Cybernetics, 110(2-3), doi:10.1007/s00422-016-0691-9. ISSN 0340-1200

In 1985, Haken, Kelso and Bunz proposed a system of coupled nonlinear oscillators as a model of rhythmic movement patterns in human bimanual coordination. Since then, the Haken–Kelso–Bunz (HKB) model has become a modelling paradigm applied extensivel... Read More

Localised auxin peaks in concentration-based transport models for plants (2015)
Journal Article
Draelants, D., Avitabile, D., & Vanroose, W. (2015). Localised auxin peaks in concentration-based transport models for plants. Interface, 12(106), doi:10.1098/rsif.2014.1407. ISSN 1742-5662

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

Calcium induced calcium release during action potential firing in developing inner hair cells (2015)
Journal Article
Iosub, R., Avitabile, D., Grant, L., Tsaneva-Atanasova, K., & Kennedy, H. J. (2015). Calcium induced calcium release during action potential firing in developing inner hair cells. Biophysical Journal, 108(5), 1003-1012. doi:10.1016/j.bpj.2014.11.3489

In the mature auditory system inner hair cells (IHCs) convert sound induced vibrations into electrical signals that are relayed to the CNS via auditory afferents. Before the cochlea can respond to normal sound levels, developing IHCs fire calcium bas... Read More

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. doi: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

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. doi: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

Spots: breathing, drifting and scattering in a neural field model (2014)
Book
Coombes, S., Schmidt, H., & Avitabile, D. (2014). Spots: breathing, drifting and scattering in a neural field model. In P. Beim Graben, S. Coombs, R. Potthast, & J. Wright (Eds.), Neural fields: theory and applicationsSpringer

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

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

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), doi:10.1137/130918721. ISSN 1064-8275

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

On the numerical continuation of isolas of equilibria
Journal Article
Avitabile, D., Desroches, M., & Rodrigues, S. (2012). On the numerical continuation of isolas of equilibria. International Journal of Bifurcation and Chaos, 22(11), doi:10.1142/S021812741250277X. ISSN 0218-1274

We present a numerical strategy to compute one-parameter families of isolas of equilibrium solutions in ODEs. Isolas are solution branches closed in parameter space. Numerical continuation is required to compute one single isola since it contains at... Read More