Equilibria of a nonlocal model for biological aggregations: linear stability and bifurcation studies

In this thesis, we study a nonlocal hyperbolic model for biological aggregations in one spatial dimension. In particular, we investigate the linear stability of the spatially homogeneous steady states and perform bifurcation studies. Two cases are considered; the first with constant velocity and the second with density-dependent velocity. We derive the dispersion relation and illustrate some examples for both cases. Numerical simulations of the model confirm the results obtained through linear stability analysis. We also provide the stability regions for some of the steady states by changing the magnitudes of attraction and repulsion and show that the instability region tends to increase in the presence of nonconstant velocities.