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We consider the effect of asynunetry in the migration, and spatial dependence of the selection process, upon the emergence and stability of such gradients.

Path tracking driver models assume the observed path deviation ahead of the vehicle to be proportionally transferred to a corrective steering input. The most simple version of such a model includes three parameters, a single preview distance, a steering gain and a delay time, being examined in this paper, in dependency of vehicle properties, driver characteristics, velocity and path. It is shown that, for different and bounded preview lengths, a driver can follow any path with almost the same minimum path error, if the gain is adapted appropriately. The upper boundary is path-dependent but driver and path characteristics have only a minor effect on the resulting relationship between preview length and gain. Consequently, gain and preview length may well vary along some path. This has been examined, experimentally, for different drivers. A too small preview length conflicts with closed-loop stability, explicitly described in terms of vehicle parameters, vehicle speed and driver delay time. The results of this paper provide a basis for enhanced understanding of human driver behaviour.

In this paper we investigate the effect of a change in geometry of a nerve axon on the propagation of potential waves along the axon. In particular we show that potential waves are stopped at a sudden large increase of cross-section area such as increase of diameter or branching. Some special examples are treated. The results do also apply to problems in population genetics and chemical reaction theory.

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