Stability Analysis of a Discrete Time Prey-Predator Population Model with Immigration

Hatice Kılıç; Nilüfer Topsakal; Figen Kangalgil

doi:10.17776/csj.779203

EN

Stability Analysis of a Discrete Time Prey-Predator Population Model with Immigration

Abstract

In this paper, a discrete-time prey-predator population model with immigration which is obtained by implementing forward Euler’s scheme has been considered. The existence of fixed points of the presented model has been investigated. Moreover, the stability analysis of the fixed points of the population model has been examined and the topological classification of the fixed points of the model has been made. Moreover, the OGY feedback control method is to implement to controlchaos caused by the Flip bifurcation. Finally, Flip bifurcation,chaos control strategy, and asymptotic stability of the only positive fixed point are verifiedwith the help of numerical simulations.

Keywords

prey-predator model, stability analysis, Immigration, Fixed point, Chaotic behavior

Supporting Institution

CÜBAP

Project Number

F-621

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Hatice Kılıç ^*
0000-0003-1566-1103
Türkiye

Nilüfer Topsakal
0000-0001-7216-044X
Türkiye

Figen Kangalgil
0000-0003-0116-8553
Türkiye

Publication Date

December 29, 2020

Submission Date

August 11, 2020

Acceptance Date

December 17, 2020

Published in Issue

Year 2020 Volume: 41 Number: 4

DOI

https://doi.org/10.17776/csj.779203

IZ

https://izlik.org/JA59ES54HE

APA

Kılıç, H., Topsakal, N., & Kangalgil, F. (2020). Stability Analysis of a Discrete Time Prey-Predator Population Model with Immigration. Cumhuriyet Science Journal, 41(4), 884-900. https://doi.org/10.17776/csj.779203

AMA

1.Kılıç H, Topsakal N, Kangalgil F. Stability Analysis of a Discrete Time Prey-Predator Population Model with Immigration. CSJ. 2020;41(4):884-900. doi:10.17776/csj.779203

Chicago

Kılıç, Hatice, Nilüfer Topsakal, and Figen Kangalgil. 2020. “Stability Analysis of a Discrete Time Prey-Predator Population Model With Immigration”. Cumhuriyet Science Journal 41 (4): 884-900. https://doi.org/10.17776/csj.779203.

EndNote

Kılıç H, Topsakal N, Kangalgil F (December 1, 2020) Stability Analysis of a Discrete Time Prey-Predator Population Model with Immigration. Cumhuriyet Science Journal 41 4 884–900.

IEEE

[1]H. Kılıç, N. Topsakal, and F. Kangalgil, “Stability Analysis of a Discrete Time Prey-Predator Population Model with Immigration”, CSJ, vol. 41, no. 4, pp. 884–900, Dec. 2020, doi: 10.17776/csj.779203.

ISNAD

Kılıç, Hatice - Topsakal, Nilüfer - Kangalgil, Figen. “Stability Analysis of a Discrete Time Prey-Predator Population Model With Immigration”. Cumhuriyet Science Journal 41/4 (December 1, 2020): 884-900. https://doi.org/10.17776/csj.779203.

JAMA

1.Kılıç H, Topsakal N, Kangalgil F. Stability Analysis of a Discrete Time Prey-Predator Population Model with Immigration. CSJ. 2020;41:884–900.

MLA

Kılıç, Hatice, et al. “Stability Analysis of a Discrete Time Prey-Predator Population Model With Immigration”. Cumhuriyet Science Journal, vol. 41, no. 4, Dec. 2020, pp. 884-00, doi:10.17776/csj.779203.

Vancouver

1.Hatice Kılıç, Nilüfer Topsakal, Figen Kangalgil. Stability Analysis of a Discrete Time Prey-Predator Population Model with Immigration. CSJ. 2020 Dec. 1;41(4):884-900. doi:10.17776/csj.779203

Cited By

Period-doubling Bifurcation and Stability in a Two Dimensional Discrete Prey-predator Model with Allee Effect and Immigration Parameter on Prey

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Stability of nonlinear population systems with individual scale and migration

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