Premium
An asymptotic result for a certain type of delay dynamic equation with biological background
Author(s) -
Koyuncuoğlu Halis Can,
Turhan Nezihe,
Adıvar Murat
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6465
Subject(s) - mathematics , dynamic equation , constant (computer programming) , mathematical analysis , function (biology) , span (engineering) , nonlinear system , computer science , biology , civil engineering , evolutionary biology , engineering , programming language , physics , quantum mechanics
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.