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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Positive Almost Periodic Solutions for a Time Scale Model of Fishery with Time Varying Variable Delays and Harvesting Term

Journal of Applied Nonlinear Dynamics 12(2) (2023) 257--271 | DOI:10.5890/JAND.2023.06.005

Mahammad Khuddush$^1$, K. Rajendra Prasad$^2$

$^1$ Department of Mathematics, Dr. Lankapalli Bullayya College of Engineering, Resapuvanipalem, Visakhapatnam, 530013, Andhra Pradesh, India

$^2$ Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, 530003, Andhra Pradesh, India

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Abstract

In this paper, we study fishing model with time varying variable delays and harvesting term on time scales, $$ \mathtt{z}^\triangle(\mathtt{s})=-\upalpha(\mathtt{s})\mathtt{z}(\mathtt{s})+ \sum_{\mathtt{j}=1}^{\mathtt{N}}\frac{\upbeta_\mathtt{j}(\mathtt{s})}{1+ (\frac{\mathtt{z}(\mathtt{s}-\uptau_\mathtt{j}(\mathtt{s}))} {\mathtt{G}(\mathtt{s})})^{\ell_\mathtt{j}}}-\mathtt{h}(\mathtt{s}),~~\mathtt{s}\in\mathbb{T}. $$ We first derive sufficient conditions for the existence of unique positive almost periodic solution for the model by applying contraction principle. In addition, with the help of Gronwall's inequality and functional analysis, we study global exponential stability and then by means of Lyapunov function, we establish asymptotical stability of the addressed model. Finally, numerical simulations are employed to illustrate the obtained results.

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