THE RELAXATION OF MAYS CONJECTURE FOR THE LOGISTIC EQUATION

When modelling a physical problem by a deterministic system, random ef fects often need to be taken into account. By including these uncertai nties, a stable equilibrium of a system is going to persist up to a po int that the variations are large enough to drive the system to instab ility at that equilibrium. By considering a simple population model, t he logistic model with uncertainty in the carrying capacity, it is pos sible to find a bound on the amount of noise required in the system to do this. The bound is a relaxation of the bound given by May's conjec ture.