We studied the motion of a random walker in two dimensions with nonuniform angular distribution
biased by an external periodic pulse. Here, we analytically calculated the mean square displacement
(end-to-end distance of a walk after n time steps), without bias and with bias. We determined the
average x -component of the final displacement of the walker. Interestingly, we noted that for a
particular periodicity of the bias, this average x -component of the final displacement becomes
approximately zero. The average y -component of the final displacement is found to be zero for any
perodicity of the bias, and its reason can be attributed to the nature of the probability density
function of the angle (subtended by the displacement vector with the x -axis). These analytical
results are also supported by computer simulations. The present study may be thought of as a model
for arresting the bacterial motion (along a preferred direction) by an external per…