Logistic equation on time scales

Abstract

We propose a new dynamic logistic equation that, in contrast with the one available in the literature, preserves the non-negativity of its solutions, which is an essential property for biological meaning. We derive the exact solution of the proposed model and analyze its behavior on arbitrary time scales. Finally, we illustrate our results with concrete examples. Our key novelty is: the model’s ability to maintain positivity across general time scales and its dynamic consistency with the classical logistic equation.