Abstract
This thesis examines the patterns in one spatial dimension that arise from the study of two predator-prey reaction diffusion systems that includes nonlocal terms. The first model considered was one proposed in Gourley & Britton (1996). However, this model was shown to have serious flaws and consequently a second, improved model was proposed. It is this second model that is the main focus of this thesis. A spatially uniform solution with constant, nonzero numbers of predator and prey exists. A linear stability study of this solution shows that both Hopf and Turing bifurcations can occur along with several types of codimension two bifurcation points. Weakly nonlinear analysis of the Hopf and Turing bifurcations are performed and the results compared with computations. An investigation of the of the codimension two points is also made: one is a Takens-Bogdanov point where both Hopf and steady-state bifurcations meet and the second where Hopf and steady-state bifurcations onset with wavenumber in the ratio 1:2.