Interplay between reproduction and age selective harvesting delays of a single population non-autonomous system

This paper is concerned with an analysis of the dynamics of a non-autonomous, single population age based growth model with harvesting formulation. First, we derive sufficient conditions for permanence and positive invariance. Then, by constructing a scalar function, namely the Lyapunov function, we...

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Bibliographic Details
Published in:arXiv.org 2020-01
Main Authors: N S N V K Vyshnavi Devi, Debaldev Jana, Lakshmanan, M
Format: Article
Language:English
Subjects:
Computer simulation
Existence theorems
Fixed points (mathematics)
Growth models
Liapunov functions
Mathematical models
Online Access:Get full text
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Summary:This paper is concerned with an analysis of the dynamics of a non-autonomous, single population age based growth model with harvesting formulation. First, we derive sufficient conditions for permanence and positive invariance. Then, by constructing a scalar function, namely the Lyapunov function, we arrive at a suitable criterion for global attractivity. With the help of Brouwer fixed point and continuation theorems, we obtain constraints for the existence of a positive periodic solution. Then we prove that there exists only one solution which is almost periodic in nature that is distinct from every other solution. Further, we carry out a numerical simulation to support the analytical findings.
ISSN:2331-8422