Dresden 2003 – scientific programme
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DY: Dynamik und Statistische Physik
DY 34: Nonlinear dynamics I
DY 34.3: Talk
Wednesday, March 26, 2003, 15:00–15:15, G\"OR/226
Trail Formation in a Directed Walker Model with Feedback — •Beatrix Schulz1, Peter Reineker2, and Michael Schulz2 — 1Fachbereich Physik, MLU Halle-Wittenberg, 06099 Halle (Saale), Germany — 2Abteilung Theoretische Physik, Uni Ulm, 89069 Ulm, Germany
Various species use an external memory for navigation, e.g. by setting chemical or visual signposts. Such an external storage of information plays an important role in establishing impressive trail systems. We apply the concept of a random walker with self induced feedback on directed walks. The directed motion of the walk reflects the tendency of animals to go forward and following a global direction, instead of frequently changing their main direction like a simple random walker. Additionally, the self induced feedback realizes the local rules of navigation. This model allows the study of indirect collective phenomenon of trail formation, which is widely spread in the world of animals and humans. The structure of the trail systems depends strongly on the microscopic realization of the feedback mechanism and on the general repulsive or attractive intercation between different pathes.
A repulsive feedback generates ergodic states, i.e. small initial structural differences of the trail system disappear in the long time limit. A nontrivial situation occurs for an attractive feedback where in the long time regime a distinct network of major trails (or only one dominant trail) appears, which is amplified by all subsequent walkers.