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Brain-wave equation incorporating axodendritic connectivity (2020)
Journal Article
Ross, J., Margetts, M., Bojak, I., Nicks, R., Avitabile, D., & Coombes, S. (2020). Brain-wave equation incorporating axodendritic connectivity. Physical Review E, 101(2), Article 022411. https://doi.org/10.1103/PhysRevE.101.022411

©2020 American Physical Society. We introduce an integral model of a two-dimensional neural field that includes a third dimension representing space along a dendritic tree that can incorporate realistic patterns of axodendritic connectivity. For natu... Read More about Brain-wave equation incorporating axodendritic connectivity.

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), Article 012313. https://doi.org/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 about Next-generation neural field model: The evolution of synchrony within patterns and waves.

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. https://doi.org/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 about Network mechanisms underlying the role of oscillations in cognitive tasks.

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, https://doi.org/10.1016/j.jmps.2018.03.025

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 about Modal nudging in nonlinear elasticity: tailoring the elastic post-buckling behaviour of engineering structures.

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 Analysis (111-121). Cham, Switzerland: Springer Nature. https://doi.org/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 about Neural Fields: Localised States with Piece-Wise Constant Interactions.

Capturing the dynamics of a hybrid multiscale cancer model with a continuum model (2018)
Journal Article
Joshi, T. V., Avitabile, D., & Owen, M. R. (2018). Capturing the dynamics of a hybrid multiscale cancer model with a continuum model. Bulletin of Mathematical Biology, 80(6), 1435–1475. https://doi.org/10.1007/s11538-018-0406-6

Cancer is a complex disease involving processes at spatial scales from sub-cellular, like cell signalling, to tissue scale, such as vascular network formation. A number of multiscale models have been developed to study the dynamics that emerge from t... Read More about Capturing the dynamics of a hybrid multiscale cancer model with a continuum model.

Exploring the design space of nonlinear shallow arches with generalised path-following (2018)
Journal Article
Cox, B. S., Groh, R. M., Avitabile, D., & Pirrera, A. (2018). Exploring the design space of nonlinear shallow arches with generalised path-following. Finite Elements in Analysis and Design, 143, https://doi.org/10.1016/j.finel.2018.01.004

The classic snap-through problem of shallow arches is revisited using the so-called generalised path-following technique. Classical buckling theory is a popular tool for designing structures prone to instabilities, albeit with limited applicability a... Read More about Exploring the design space of nonlinear shallow arches with generalised path-following.

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), https://doi.org/10.1137/17M1120932

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 about Spot dynamics in a reaction-diffusion model of plant root hair initiation.

Generalised path-following for well-behaved nonlinear structures (2017)
Journal Article
Groh, R., Avitabile, D., & Pirrera, A. (2018). Generalised path-following for well-behaved nonlinear structures. Computer Methods in Applied Mechanics and Engineering, 331, https://doi.org/10.1016/j.cma.2017.12.001

Recent years have seen a research revival in structural stability analysis. This renewed interest stems from a paradigm shift regarding the role of buckling instabilities in engineering design—from detrimental sources of catastrophic failure to novel... Read More about Generalised path-following for well-behaved nonlinear structures.

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), Article 052407. https://doi.org/10.1103/PhysRevE.96.052407

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 about Synchrony-induced modes of oscillation of a neural field model.

Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system (2017)
Journal Article
Avitabile, D., Desroches, M., Knobloch, E., & Krupa, M. (in press). Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2207), https://doi.org/10.1098/rspa.2017.0018

A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of solutions de... Read More about Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system.

The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions (2017)
Journal Article
Gökçe, A., Avitabile, D., & Coombes, S. (2017). The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions. Journal of Mathematical Neuroscience, 7(1), Article 12. https://doi.org/10.1186/s13408-017-0054-4

© 2017, The Author(s). 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 unbounde... Read More about The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions.

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), https://doi.org/10.1103/PhysRevE.95.042205

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 about Spatio-temporal canards in neural field equations.

Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis (2017)
Journal Article
Avitable, D., & Wedgwood, K. C. A. (in press). Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis. Journal of Mathematical Biology, 75(4), https://doi.org/10.1007/s00285-016-1070-9

We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling... Read More about Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis.

Beyond in-phase and anti-phase coordination in a model of joint action (2016)
Journal Article
Avitabile, D., S?owi?ski, 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), https://doi.org/10.1007/s00422-016-0691-9

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 about Beyond in-phase and anti-phase coordination in a model of joint action.

Localized auxin peaks in concentration-based transport models of the shoot apical meristem (2015)
Journal Article
Draelants, D., Avitabile, D., & Vanroose, W. (2015). Localized auxin peaks in concentration-based transport models of the shoot apical meristem. Interface, 12(106), Article 20141407. https://doi.org/10.1098/rsif.2014.1407

© 2015 The Author(s) Published by the Royal Society. All rights reserved. We study the formation of auxin peaks in a generic class of concentration-based auxin transport models, posed on static plant tissues. Using standard asymptotic analysis, we pr... Read More about Localized auxin peaks in concentration-based transport models of the shoot apical meristem.

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. https://doi.org/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 about Calcium induced calcium release during action potential firing in developing inner hair cells.

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.