### Mathematical Biosciences and Engineering

2021, Issue 5: 6819-6840. doi: 10.3934/mbe.2021339
Research article Special Issues

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

• 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.

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

### Related Papers:

• 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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