Playing Catch-Up with Iterated Exponentials
R. L. Devaney, Krešimir Josić́, Mónica Moreno Rocha, P. Seal, Y. Shapiro, A. T. Frumosu · American Mathematical Monthly · 2004
Abstract Assume a predator-prey system where the step size of both speciesgrows as iterated exponentials. Suppose the predator gives the prey an initial advantage before starting the chase. Will the prey escape the preda-tor? We provide conditions on the step size to determine if the predator will catch up with the prey. 1 Introduction Suppose that we have two animals that make the same number of strides per minute, but one of them makes larger strides than the other. If the strides of the smaller animal (the prey) have length a, and those of the larger animal (the predator) have length b, it is easy to see that a persistent predator will always be able to catch up with its prey. Let us assume that the prey starts one step ahead of the predator. After n steps the distance between the two is nb \\Gamma (n + 1)a = n(b \\Gamma a) \\Gamma a and consequently, if n? a=(b \\Gamma a), the predator will have overtaken its prey.