- Correction
- Open Access
- Published:

# Correction to: Global and local stability analysis in a nonlinear discrete-time population model

*Advances in Difference Equations*
**volume 2018**, Article number: 357 (2018)

## Correction

In the publication of Ref. [1], there are some errors. These are identified and corrected in this article.

1. In the abstract:

The error “We conclude that the Allee effect decreases both local stability and global stability of equilibrium points of the population dynamic model.” should instead read: “We conclude that the Allee effect decreases the local stability of the equilibrium point of the population dynamic model but increases the global stability of the equilibrium point of the population dynamic model.”

2. Page 2, line 18:

The error “(i) \(f' ( N_{t} )<0\) for \(N_{t} \in[0,\infty)\); …” should instead read: “(i) \(f'\) is continuous and \(f' ( N_{t} )<0\) for \(N_{t} \in[0,\infty)\); ….”

3. Page 2, line 31:

The error “(iv) The Allee effect increases as density increases…” should instead read: “(iv) The Allee effect decreases as the density increases….”

4. Theorem 5 should instead read:

### Theorem 1

*Let*
\(N^{*}\)
*be a positive equilibrium point of* (2) *by the Allee effect at time*
*t*
*with respect to*
\(r^{*}\). *Then*
\(N^{*}\)
*is locally stable if the inequality*

*holds*.

### Proof

From (i)–(v), we can say that \(F_{\alpha}'\) is a continuous function. The linearized form of (2) in a neighbourhood of \(N^{*}\) is given by

such that \(u_{t} = N_{t} - N^{*}\). By applying Theorem 2, we have

5. Page 6, lines 23, 24, 25:

The statement “Note that \(F_{l, a} >0\) is always true from Theorem 5. Namely, \(- r [ 1+ N^{*} \frac{\alpha' ( N^{*} )}{\alpha( N^{*} )} ] < f' ( N^{*} )\) is always provided. Since this inequality is related with \(r [ 1+ N^{*} \frac{\alpha' ( N^{*} )}{\alpha( N^{*} )} ] <1\), we must take this inequality as stability conditions.” is incorrect.

6. Page 7, line 1:

The error “Corollary 11 The Allee effect at time *t* decreases the global stability…” should instead read: “Corollary 11 The Allee effect at time *t* increases the global stability….”

7. Page 8, line 2 below:

The error “Consequently, the Allee effect decreases the local stability and the global stability of the equilibrium points of (1).” should instead read: “Consequently, the Allee effect decreases the local stability of the equilibrium point of (1) but increases the global stability of the equilibrium point of (1).”

8. Page 7, line 5:

The error “\(-1-r< f(N^{*})<-r\)” should instead write: “\(-1-r< f'(N^{*})<-r\)”.

9. Page 7, line 15:

The error “So, we confirm that the Allee effect decreases the local stability and global stability…” should instead read: “So, we confirm that the Allee effect decreases the local stability but increases the global stability of the equilibrium point of the population model.”.

The author would like to apologize for these errors and for any inconvenience caused.

## References

Ak Gümüş, Ö.: Global and local stability analysis in a nonlinear discrete-time population model. Adv. Differ. Equ.

**2014**, 299 (2014). https://doi.org/10.1186/1687-1847-2014-299

## Author information

### Authors and Affiliations

### Contributions

The author read and approved the final manuscript.

### Corresponding author

## Ethics declarations

### Competing interests

The author declares to have no competing interests.

## Additional information

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The online version of the original article can be found under https://doi.org/10.1186/1687-1847-2014-299.

## Rights and permissions

**Open Access** This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## About this article

### Cite this article

Ak Gümüş, Ö. Correction to: Global and local stability analysis in a nonlinear discrete-time population model.
*Adv Differ Equ* **2018**, 357 (2018). https://doi.org/10.1186/s13662-018-1812-7

Received:

Accepted:

Published:

DOI: https://doi.org/10.1186/s13662-018-1812-7