Food web chaos without subchain oscillators

A basic food web of four species is considered, of which there is a bottom prey X, two competing predators V, Z on X, and a super predator W only on Y. The main finding is that population chaos does not require the existence of oscillators in any subsystem of the web. This minimum population chaos is demonstrated by increasing the relative reproductive rate of Z alone without alternating any other parameter nor any nullcline of the system. It occurs as the result of a period-doubling cascade from a Hopf bifurcation point. The method of singular perturbation is used to determine the Hopf bifurcation involved as well as the parameter values.