A note on a camouflage pursuit problem

Abstract

Motion camouflage is a pursuit strategy whereby a predator moves towards a prey while appearing stationary to the prey except for the change in its perceived cross section as it approaches. If the effect of cross section size with distance is ignored then this means that the target is unable to discern that the aggressor is moving. The aggressor appears to be at its initial position or is camouflaged by a stationary object in the background. We shall derive a closed form solution to the problem of camouflage pursuit for a particular situation. Although general differential equations have already been derived for this strategy they have not been solved in closed form.