Positive Almost Periodic Solutions for a Time Scale Model of Fishery with Time Varying Variable Delays and Harvesting Term - Khuddush, Mahammad; Prasad, K. Rajendra (Journal of Applied Nonlinear Dynamics, 2026)
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.