In this paper, we consider a delayed discrete single population patch model in advective environments. The individuals are subject to both random and directed movements, and there is a net loss of individuals at the downstream end due to the flow into a lake. Choosing time delay as a bifurcation parameter, we show the existence of Hopf bifurcations for the model. In homogeneous non-advective environments, it is well known that the first Hopf bifurcation value is independent of the dispersal rate. In contrast, for homogeneous advective environments, the first Hopf bifurcation value depends on the dispersal rate. Moreover, we show that the first Hopf bifurcation value in advective environments is larger than that in non-advective environments if the dispersal rate is large or small, which suggests that directed movements of the individuals inhibit the occurrence of Hopf bifurcations.

In this paper we develop a compilant system that permits robotic assembly of chamferless pieces. The idea is to absorb the positioning error between parts to be inserted by giving one of them a planar random movement. An actuator consisting of two axes (X and y) operated by an electromagnetic System is fitted to the work table; when its inputs are pseudo-random binary signais (P.R.B.S.) random motion is obtained. The trajectories of the actuator are analysed depending upon the P.R.B.S. parameters and a peg-in-a-hole assembly task is carried out. Experimental results show that large positioning errors can be compensated for chamferless insertions.