THE SQUARE-WAVE TYPE FUNCTIONS AS A LIMIT OF SOLUTIONS OF 3 MATHEMATICAL-MODELS

Three mathematical models for biological phenomena are studied. All the models are particular cases of the delay differential equation x(t) = -lambdax(t) + lambdaf(x(t - 1)), f : R --> R, lambda > 0. It is shown that, for lambda tending to infinity, under mild conditions of f (i.e., f has a stable 2-periodic orbit), the periodic solutions of these models converge to a ''square wave'' type function whose levels are determined by the two-periodic orbit of each particular f. At the same time, as f is a function that depends on the parameters lambda is-an-element-of R+* and mu is-an-element-of R+*, it is possible to determine numerically, with calculus involving the parameters, regions of stability for the solutions when lambda and mu vary in determined regions.