| Abstract: |
| Spatial memory is a key feature driving the movement of mobile organisms. A key tool for modelling movement in response to remembered space use is via an advection term in a partial differential equation (PDE). We use a reaction-diffusion-advection model to describe the movement of an animal species, with a non-local advection term driven by a cognitive map representing memory of past animal locations embedded in the environment. The global existence and boundedness of solutions are shown, and the existence of spatial patterns formed in the model are rigorously proved using spectral analysis and bifurcation methods. |
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