A COMPARISON OF THE BEHAVIOR OF SOLUTIONS OF THE TWO LOGISTIC DYNAMIC EQUATIONS ON TIME SCALES

摘要

We examine the behavior of the two so-called logistic equations on time scales. It is well-known that solutions of the dynamic logistic equation x~Δ = [p(Θ) (fx)]x behave very similarly to solutions of the classic logistic differential equation, regardless of time scale. The focus of this work is on the behavior of the solutions of the other dynamic logistic equation, y~Δ = [(Θ)(-p + fy)]y, on T = hZ. Conditions are given when the behavior is much like that of the classic logistic differential equation, and in this case the two dynamic logistic equations are compared. However, there are numerous cases, depending on the choice of h, in which the solutions of the logistic equation y~Δ = [(Θ)(-p + fy)]y behave substantially different than those of x~Δ = [p (Θ) (fx)]x. These cases are enumerated and explored.