Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Bifurcation dynamics in models for self-organised biological aggregations
Raluca Eftimie

Last modified: 2014-06-09


Understanding the mathematical mechanisms behind the patterns and the transitions between patterns exhibited by self-organising individuals is an important step in understanding the collective behavior of these individuals. Here, we use a correlated random walk approach to derive a class of nonlocal hyperbolic models for self-organised biological aggregations. Then, we discuss the variety of complex spatial and spatio-temporal patterns exhibited by these models. To investigate the formation of some of these patterns that appear via codimension-1 and codimension-2 bifurcations, we perform weakly nonlinear analysis. We show that while many patterns occur for different parameter values, there are other patterns that occur for similar parameter values. In this latter case, the transition between the patterns is intrinsic to the system, being associated with perturbations in the system (and not with changes in parameter values characterising individuals' behaviour: speed, turning rates, social interactions).