Follow the yellow-brick road. Self-organized path formation: heterogeneity in population movement and distribution.
09/3/10, 13:30 at Room 3631 (6th floor of building 3 of the Faculty of Sciences)
Since animals can move by their own will, they try to optimise the length and the comfort of their displacements. Indeed, if one had to make a journey, one would intuitively choose to move in the most comfortable environment as long as the direction is correct. More than just using existing habitat features, many animals including humans are capable of modifying the environment, e.g., creating and using paths to optimize their travel. It is plausible that the resulting modification of the landscape can affect the spread of the population by providing a network of persistent travel paths (trails or roads) along which the spread is accelerated. Here we suggest a simple heuristic model describing the development of paths in a uniform habitat, so that the path pattern is not imposed externally (e.g., by terrain features) but is rather produced spontaneously by the moving individuals. The model uses the directions of the maximum and minimum curvatures of a scalar field standing for the ease of movement. Simulations show the creation of paths system emerging from uniform initial condition with a small noise to break symmetry. Population occupies space heterogeneously, as opposed as the uniform pattern generated with the largely used Fisher-Kolmogorov equation. Furthermore, front propagation of the population is affected by the formation of paths and breaks down into several paths heads, changing therefore the picture of a linear front of propagation.
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