Trail formation and condensation of trajectories in a direct walker model with feedback

A directed walker model with external memory is studied by numerical simulations and statistical approaches. The structure of the trail systems depends strongly on the microscopic realization of the feedback mechanism and on the general repulsive or attractive interaction between different paths. Especially, we find nonergodic behavior for kinetic attraction and an ergodic one for repulsive interaction. The strong attraction regime shows a pronounced condensation of trajectories to one common path.