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| Parabolic and hyperbolic models have been used intensively over the past years to describe the formation and movement of self-organised biological aggregations. Here we use symmetry and bifurcation theory to investigate a class on nonlocal hyperbolic models and their parabolic counterparts. We show that the parabolic models exhibit a loss of bifurcation dynamics (i.e., loss of Hopf bifurcations) compared to the hyperbolic models (which can exhibit both codimension-1 and codimension-2 bifurcations: Hopf, steady-state, Hopf/Hopf, Hopf/steady-state and steady-state/steady-state bifurcations). This explains the less rich patterns exhibited by the parabolic equations for self-organised aggregations. |
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