Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment

Rizwan Ahmed; Shehraz Akhtar

doi:10.32323/ujma.1167907

EN

Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment

Abstract

We studied a host-parasite model qualitatively. The host-parasitoid model is obtained by modifying the Nicholson-Bailey model so that the number of hosts that parasitoids can't attack is fixed. Topological classification of equilibria is achieved with the implementation of linearization. Furthermore, Neimark-Sacker bifurcation is explored using the bifurcation theory of normal forms at interior steady-state. The bifurcation in the model is controlled by implementing two control strategies. The theoretical studies are backed up by numerical simulations, which show the conclusions and their importance.

Keywords

Bifurcation, Chaos control, Nicholson-Bailey model, Stability

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Rizwan Ahmed ^*
Pakistan

Shehraz Akhtar
Pakistan

Publication Date

March 28, 2023

Submission Date

August 28, 2022

Acceptance Date

January 5, 2023

Published in Issue

Year 2023 Volume: 6 Number: 1

DOI

https://doi.org/10.32323/ujma.1167907

IZ

https://izlik.org/JA95DJ38GY

APA

Ahmed, R., & Akhtar, S. (2023). Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment. Universal Journal of Mathematics and Applications, 6(1), 30-42. https://doi.org/10.32323/ujma.1167907

AMA

1.Ahmed R, Akhtar S. Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment. Univ. J. Math. Appl. 2023;6(1):30-42. doi:10.32323/ujma.1167907

Chicago

Ahmed, Rizwan, and Shehraz Akhtar. 2023. “Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment”. Universal Journal of Mathematics and Applications 6 (1): 30-42. https://doi.org/10.32323/ujma.1167907.

EndNote

Ahmed R, Akhtar S (March 1, 2023) Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment. Universal Journal of Mathematics and Applications 6 1 30–42.

IEEE

[1]R. Ahmed and S. Akhtar, “Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment”, Univ. J. Math. Appl., vol. 6, no. 1, pp. 30–42, Mar. 2023, doi: 10.32323/ujma.1167907.

ISNAD

Ahmed, Rizwan - Akhtar, Shehraz. “Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment”. Universal Journal of Mathematics and Applications 6/1 (March 1, 2023): 30-42. https://doi.org/10.32323/ujma.1167907.

JAMA

1.Ahmed R, Akhtar S. Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment. Univ. J. Math. Appl. 2023;6:30–42.

MLA

Ahmed, Rizwan, and Shehraz Akhtar. “Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment”. Universal Journal of Mathematics and Applications, vol. 6, no. 1, Mar. 2023, pp. 30-42, doi:10.32323/ujma.1167907.

Vancouver

1.Rizwan Ahmed, Shehraz Akhtar. Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment. Univ. J. Math. Appl. 2023 Mar. 1;6(1):30-42. doi:10.32323/ujma.1167907