Interplay Between Reproduction and Age Selective Harvesting Delays of a Single Population Non-Autonomous System

N. S. N. V. K. Vyshnavi Devi (), Debaldev Jana () and M. Lakshmanan ()
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N. S. N. V. K. Vyshnavi Devi: SRM Institute of Science and Technology
Debaldev Jana: SRM Institute of Science and Technology
M. Lakshmanan: Bharathidasan University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1857-1891

Abstract: Abstract 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.

Keywords: Non-autonomous dynamical system; age-structured model; permanence; periodic solution; global attractivity; almost periodic solution; 37B55; 92D25; 92D40 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0501-x

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