This study investigates the conditional Hyers–Ulam stability of a first-order nonlinear hdifference
equation, specifically a discrete logistic model. Identifying bounds on both the relative
size of the perturbation and the initial population size is an important issue for nonlinear Hyers–Ulam
stability analysis. Utilizing a novel approach, we derive explicit expressions for the optimal lower
bound of the initial value region and the upper bound of the perturbation amplitude, surpassing the
precision of previous research. Furthermore, we obtain a sharper Hyers–Ulam stability constant, which
quantifies the error between true and approximate solutions, thereby demonstrating enhanced stability.
The Hyers–Ulam stability constant is proven to be in terms of the step-size h and the growth rate but
independent of the carrying capacity. Detailed examples are provided illustrating the applicability and
sharpness of our results on conditional stability. In addition, a sensitivity analysis of the parameters
appearing in the model is also performed.
