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## Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system

#### Figen KANGALGİL [1] , Seval IŞIK [2]

This article is about a discrete-time predator-prey model obtained by the forward Euler method. The stability of the fixed point of the model and the existence conditions of the Neimark-Sacker bifurcation are investigated. In addition, the direction of the Neimark-Sacker bifurcation is given. Moreover, OGY control method is to implement to control chaos caused by the Neimark-Sacker bifurcation. Finally, Neimark-Sacker bifurcation, chaos control strategy, and asymptotic stability of the only positive fixed point are verified with the help of numerical simulations. The existence of chaotic behavior in the model is confirmed by computing of the maximum Lyapunov exponents.
Predator-Prey Model, Fixed Point, Stability, Neimark-Sacker Bifurcation, Chaotic Behavior, OGY feedback control method
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Primary Language en Mathematics Mathematics Orcid: 0000-0003-0116-8553Author: Figen KANGALGİL (Primary Author)Institution: DOKUZ EYLUL UNIVERSITYCountry: Turkey Orcid: 0000-0002-6523-7805Author: Seval IŞIK Institution: CUMHURIYET UNIVERSITYCountry: Turkey Publication Date : October 6, 2020
 Bibtex @research article { hujms531024, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1761 - 1776}, doi = {10.15672/hujms.531024}, title = {Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system}, key = {cite}, author = {Kangalgi̇l, Figen and Işık, Seval} } APA Kangalgi̇l, F , Işık, S . (2020). Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system . Hacettepe Journal of Mathematics and Statistics , 49 (5) , 1761-1776 . DOI: 10.15672/hujms.531024 MLA Kangalgi̇l, F , Işık, S . "Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1761-1776 Chicago Kangalgi̇l, F , Işık, S . "Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1761-1776 RIS TY - JOUR T1 - Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system AU - Figen Kangalgi̇l , Seval Işık Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.531024 DO - 10.15672/hujms.531024 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1761 EP - 1776 VL - 49 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.531024 UR - https://doi.org/10.15672/hujms.531024 Y2 - 2020 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system %A Figen Kangalgi̇l , Seval Işık %T Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 5 %R doi: 10.15672/hujms.531024 %U 10.15672/hujms.531024 ISNAD Kangalgi̇l, Figen , Işık, Seval . "Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system". Hacettepe Journal of Mathematics and Statistics 49 / 5 (October 2020): 1761-1776 . https://doi.org/10.15672/hujms.531024 AMA Kangalgi̇l F , Işık S . Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1761-1776. Vancouver Kangalgi̇l F , Işık S . Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1761-1776.

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