An asymptotic result for a certain type of delay dynamic equation with biological background

Inspired by Cooke and York's work, we concentrate on the delay dynamic equationx Δ ( t ) = g t , x ( t ) − g t , x δ ( t )on a nonempty, arbitrary, closed set of real numbers, so‐called a time scale. The utilization of an abstract delay function δ in the above‐given equation relaxes the condition that each individual has a fixed constant life span when it fits a growth process. The main result is obtained by establishing a linkage between the delay dynamic equation and an integral equation. By constructing a phase space for a given initial function, we show the unique solution converges to a predetermined constant.