Global attractivity and periodic solutions in delay-differential equations related to models in physiology and population biology

With appropriate assumptions, the following two general first-order nonlinear differential delay equations may be employed to describe some physiological control systems as well as some population growth processes: {Mathematical expression} and {Mathematical expression} It is assumed that g(x) is strictly increasing, g(0)=0, and each of these two equations has a unique positive steady state. Sufficient conditions are obtained for this steady state to be a global attractor (with respect to continuous positive initial functions) when f(x) is monotone or has only one hump. We also establish the global existence of periodic solutions in these equations.