The role of communication mechanisms on the movement of self-organised biological aggregations with nonlocal interactions
Raluca Eftimie (University of Dundee)
Thursday 26th April, 2012 14:00-15:00 Maths & Stats Bldg, LT 325
Aggregation and traffic-like movement are two of the most common collective behaviours observed in populations of cells, bacteria, animals, and even humans. These behaviours lead to the formation of a large variety of group patterns: from stationary aggregations formed of resting organisms, to zigzagging flocks of birds, or rippling waves observed in bacterial colonies. Here, we discuss a class of non-local hyperbolic models derived to reproduce and further investigate some of these aggregation patterns. The models, which incorporate non-local social interactions among group members, have been shown to display a wide range of spatial and spatiotemporal patterns: from simple stationary and travelling pulses, to more complex patterns such as ripples, zigzags and breathers. Intensive numerical simulations could provide some understanding of the biological mechanisms behind these patterns. The mathematical mechanisms that generate certain patterns can be investigated, for example, using bifurcation theory or travelling wave theory. In particular, we focus on travelling pulses, and show that the movement and shape of these pulses is influenced by social interactions as well as communication mechanisms. We calculate analytically and numerically the speed of travelling pulses, and show that organisms travel at the maximum possible speed, independent of the communication mechanisms used. However, communication mechanisms combined with social interactions can influence the movement direction of travelling groups.