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A master stability function approach to cardiac alternans (2019)
Journal Article
Lai, Y. M., Veasy, J., Coombes, S., & Thul, R. (2019). A master stability function approach to cardiac alternans. Applied Network Science, 4(1), https://doi.org/10.1007/s41109-019-0199-z

During a single heartbeat, muscle cells in the heart contract and relax. Under healthy conditions, the behaviour of these muscle cells is almost identical from one beat to the next. However, this regular rhythm can be disturbed giving rise to a varie... Read More about A master stability function approach to cardiac alternans.

Synchrony in networks of Franklin bells (2019)
Journal Article
Sayli, M., Lai, Y. M., Thul, R., & Coombes, S. (2019). Synchrony in networks of Franklin bells. IMA Journal of Applied Mathematics, 84(5), 1001-1021. https://doi.org/10.1093/imamat/hxz023

The Franklin bell is an electro-mechanical oscillator that can generate a repeating chime in the presence of an electric field. Benjamin Franklin famously used it as a lightning detector. The chime arises from the impact of a metal ball on a metal be... Read More about Synchrony in networks of Franklin bells.

Complex patterns of subcellular cardiac alternans (2019)
Journal Article
Veasy, J., Lai, Y. M., Coombes, S., & Thul, R. (2019). Complex patterns of subcellular cardiac alternans. Journal of Theoretical Biology, 478, 102-114. doi:10.1016/j.jtbi.2019.06.016

Cardiac alternans, in which the membrane potential and the intracellular calcium concentration exhibit alternating durations and peak amplitudes at consecutive beats, constitute a precursor to fatal cardiac arrhythmia such as sudden cardiac death. A... Read More about Complex patterns of subcellular cardiac alternans.

Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony (2018)
Journal Article
Yi Ming, L., Thul, R., & Coombes, S. (2018). Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony. European Physical Journal - Special Topics, 227(10-11), 1251-1265. doi:10.1140/epjst/e2018-800033-y

Integrate-and-fire networks have proven remarkably useful in modelling the dynamics of real world phenomena ranging from earthquakes, to synchrony in neural networks, to cascading activity in social networks. The reset process means that such models... Read More about Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony.

Networks of piecewise linear neural mass models (2018)
Journal Article
Coombes, S., Lai, Y. M., Sayli, M., & Thul, R. (2018). Networks of piecewise linear neural mass models. European Journal of Applied Mathematics, 29(Special issue 5), 869-890. doi:10.1017/S0956792518000050

Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ordinary differential equations with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlase... Read More about Networks of piecewise linear neural mass models.

Population density equations for stochastic processes with memory kernels (2017)
Journal Article
Lai, Y. M., & de Kamps, M. (2017). Population density equations for stochastic processes with memory kernels. Physical Review E, 95, doi:10.1103/PhysRevE.95.062125

We present a method for solving population density equations (PDEs)–-a mean-field technique describing homogeneous populations of uncoupled neurons—where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. Th... Read More about Population density equations for stochastic processes with memory kernels.