Global attractors, extremal stability and periodicity for a delayed population model with survival rate on time scales

Jaqueline G. Mesquita; Urszula Ostaszewska; Ewa Schmeidel; Małgorzata Zdanowicz; Jaqueline G. Mesquita; Urszula Ostaszewska; Ewa Schmeidel; Małgorzata Zdanowicz

doi:10.3934/mbe.2021339

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 5: 6819-6840. doi: 10.3934/mbe.2021339

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Global attractors, extremal stability and periodicity for a delayed population model with survival rate on time scales

1.
Universidade de Brasília, Campus Universitário Darcy Ribeiro, Asa Norte 70910-900, Brasília-DF, Brazil
2.
University of Bialystok, ul. Ciołkowskiego 1M, 15-245 Białystok, Poland

Received: 22 June 2021 Accepted: 22 July 2021 Published: 13 August 2021

In this paper, we investigate the existence of global attractors, extreme stability, periodicity and asymptotically periodicity of solutions of the delayed population model with survival rate on isolated time scales given by

$ x^{\Delta} (t) = \gamma(t) x(t) + \dfrac{x(d(t))}{\mu(t)}e^{r(t)\mu(t)\left(1 - \frac{x(d(t))}{\mu(t)}\right)}, \ \ t \in \mathbb T. $

We present many examples to illustrate our results, considering different time scales.
- delayed population model,
- time scales,
- global attractors,
- stability,
- periodicity
Citation: Jaqueline G. Mesquita, Urszula Ostaszewska, Ewa Schmeidel, Małgorzata Zdanowicz. Global attractors, extremal stability and periodicity for a delayed population model with survival rate on time scales[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 6819-6840. doi: 10.3934/mbe.2021339

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Abstract

In this paper, we investigate the existence of global attractors, extreme stability, periodicity and asymptotically periodicity of solutions of the delayed population model with survival rate on isolated time scales given by

$ x^{\Delta} (t) = \gamma(t) x(t) + \dfrac{x(d(t))}{\mu(t)}e^{r(t)\mu(t)\left(1 - \frac{x(d(t))}{\mu(t)}\right)}, \ \ t \in \mathbb T. $

We present many examples to illustrate our results, considering different time scales.

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