Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity

Debasis Mukherjee

doi:10.33187/jmsm.1177403

EN

Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity

Abstract

This paper analyses a discrete-time Michaelis-Menten type harvested fishery model in the presence of toxicity. Boundary and interior (positive) fixed points are examined. Using an iteration scheme and the comparison principle of difference equations, we determined the sufficient condition for global stability of the interior fixed point. It is shown that the sufficient criterion for Neimark-Sacker bifurcation and flip bifurcation can be established. It is observed that the system behaves in a chaotic manner when a specific set of system parameters is selected, which are controlled by a hybrid control method. Examples are cited to illustrate our conclusions.

Keywords

Bifurcation, Chaos control, Global stability, Michaelis-Menten type harvesting, Toxicity

References

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Details

Primary Language

English

Subjects

Mathematical Sciences, Applied Mathematics (Other)

Journal Section

Research Article

Authors

Debasis Mukherjee ^*
0000-0002-5149-5985
India

Publication Date

August 7, 2023

Submission Date

September 19, 2022

Acceptance Date

March 17, 2023

Published in Issue

Year 2023 Volume: 6 Number: 2

DOI

https://doi.org/10.33187/jmsm.1177403

IZ

https://izlik.org/JA83WP47EG

APA

Mukherjee, D. (2023). Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity. Journal of Mathematical Sciences and Modelling, 6(2), 65-75. https://doi.org/10.33187/jmsm.1177403

AMA

1.Mukherjee D. Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity. Journal of Mathematical Sciences and Modelling. 2023;6(2):65-75. doi:10.33187/jmsm.1177403

Chicago

Mukherjee, Debasis. 2023. “Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity”. Journal of Mathematical Sciences and Modelling 6 (2): 65-75. https://doi.org/10.33187/jmsm.1177403.

EndNote

Mukherjee D (August 1, 2023) Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity. Journal of Mathematical Sciences and Modelling 6 2 65–75.

IEEE

[1]D. Mukherjee, “Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity”, Journal of Mathematical Sciences and Modelling, vol. 6, no. 2, pp. 65–75, Aug. 2023, doi: 10.33187/jmsm.1177403.

ISNAD

Mukherjee, Debasis. “Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity”. Journal of Mathematical Sciences and Modelling 6/2 (August 1, 2023): 65-75. https://doi.org/10.33187/jmsm.1177403.

JAMA

1.Mukherjee D. Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity. Journal of Mathematical Sciences and Modelling. 2023;6:65–75.

MLA

Mukherjee, Debasis. “Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity”. Journal of Mathematical Sciences and Modelling, vol. 6, no. 2, Aug. 2023, pp. 65-75, doi:10.33187/jmsm.1177403.

Vancouver

1.Debasis Mukherjee. Qualitative Study of a Discrete-Time Harvested Fishery Model in the Presence of Toxicity. Journal of Mathematical Sciences and Modelling. 2023 Aug. 1;6(2):65-7. doi:10.33187/jmsm.1177403