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

Document Type

Article

Publication Date

8-1-2020

Abstract

Inspired by Cooke and York's work, we concentrate on the delay dynamic equation (Formula presented.) on a nonempty, arbitrary, closed set of real numbers, so-called a time scale. The utilization of an abstract delay function ? 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.

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