Conveners
Nonlocal models in biology
- Carlo Laing ()
Description
Many models in biology and elsewhere include only local spatial interactions via e.g. diffusion, whereas nonlocal interactions sometimes provide a more realistic way of modelling the phenomenon of interest. Speaking generally, more mathematical theory has been developed for systems with local rather than nonlocal interactions. This minisymposium will bring together four very different systems all governed by nonlocal interactions, to explore the similarities and differences between them.
Many PDE-based models of collective cell behaviour implicitly assume that the population of cells is ‘well mixed’. This is called a spatial mean-field assumption. In reality, populations often have a more complex spatial structure, such as clusters and/or spatial segregation of cells. This spatial structure is both a cause and an effect of non-local interactions among cells and can make a...
Recently, nonlocal interactions (spatial long range interactions) have attracted attention in many fields. Mathematical treatment of nonlocal interaction is mainly based on convolution with kernels. If the profile of a nonlocal interaction is detected by experiments, we can easily investigate how patterns are generated by numerical simulations. However, nonlocal interactions are often...
Experimental studies have begun revealing essential properties of the structural connectivity and the spatiotemporal activity dynamics of cortical microcircuits. To integrate these properties from anatomy and physiology, and to elucidate the mechanistic links between them, we develop a cortical microcircuit model that captures a range of realistic features of synaptic connectivity. We show...
We consider a network of coupled excitatory and inhibitory theta neurons which is capable of supporting stable spatially-localised “bump” solutions. We randomly add long-range and simultaneously remove short-range connections within the network to form a small-world network and investigate the effects of this rewiring on the existence and stability of the bump solution. We consider two limits...