A Relaxed Lyapunov–Razumikhin Theorem for Retarded Differential Equation on Time Scale: Application to Single-Species System

This article investigates the retarded differential equation on time scales and presents several criteria on uniform (asymptotic) stability by the relaxed Lyapunov–Razumikhin method. Allowing the Lyapunov–Razumikhin function (LRF) to possess an indefinite or positive definite
$\Delta $
-derivative is the main novelty of this article. Furthermore, the obtained uniform (asymptotic) stability criteria are used to solve the stabilization problem of single-species system with time delay. As an application of the established stability criteria, we present one numerical example of a uniformly stable single-species system.