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Corrigendum to “Persistence and Stability analysis of discrete-time predator-prey models: a study of population and evolutionary dynamics”, Journal of Difference Equations and Applications, 25(2019), 1568–1603

First , in the statements of Lemma 2.3 and Lemma 3.10, and the proofs of Lemma 2.4, Theorem 2.5 and Theorem 3.12, we incorrectly state thatA andA are global attractors for the 2D and 3Dmodels, respectively. The correct statements of Lemma 2.3 and Lemma 3.10 should have been that there exist bounded sets ⊂ A and ⊂ A that are global attractors for the 2D and 3D models, respectively. In addition, in the proofs of Lemmas 2.3 and 3.10, we incorrectly state thatA andA are invariant instead of stating that they are positively invariant. Thus, to remedy the proofs of Lemmas 2.3 and 3.10, notice that one can show using Theorem 2.9 in [3] that for the 2D model given in (1) and for the 3D model given in (5) there exist bounded sets ⊂ A and ⊂ A that are invariant and hence are global attractors. We remark thatA andA are globally attracting sets. Accordingly, in the proofs of Lemma 2.4, Theorem 2.5 and Theorem 3.12, A and A represent compact globally attracting sets rather than global attractors. Next, the proof of Lemma 3.7 relies on an assumption not explicitly given in the statement of the lemma. The correct statement of the lemma is as follows: