A CONJECTURE TO THE SOLUTION OF THE CONTINUOUS LOGISTIC EQUATION

Abstract

Chaotic models as a rule are based on nonlinear recursive discrete equations, often illustrated by the logistic equation. In this paper, a conjecture is presented that gives an approximate solution to the continuous logistic equation. It is shown that if certain chaotic models are viewed as continuous rather than discrete, the strict borderline mathematical concept of the onset of chaos no longer retains its importance in some practical problems. In fact, it is more important to look at the degree of chaos, as illustrated in two medical problems dealing with blood flow and heart rate variability. The chaotic modeling approach is seen to be useful in analyzing experimental data.