Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation

Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation

Selective harvesting plays an important role on the dynamics of predator-prey interaction. On the other hand, the effect of predator self-limitation contributes remarkably to the stabilization of exploitative interactions. Keeping in view the selective harvesting and predator self-limitation, a disc...

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Main Authors: Zhihua Chen, Qamar Din, Muhammad Rafaqat, Umer Saeed, Muhammad Bilal Ajaz
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2020/6737098
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spelling doaj-671790deb1f24989ac4fc0fce2370a322020-11-25T03:45:22ZengHindawi LimitedJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/67370986737098Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-LimitationZhihua Chen0Qamar Din1Muhammad Rafaqat2Umer Saeed3Muhammad Bilal Ajaz4Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaDepartment of Mathematics, University of Poonch, Rawalakot, Azad Kashmir, PakistanDepartment of Mathematics and Statistics, University of Lahore, Lahore 54000, PakistanNUST Institute of Civil Engineering, School of Civil and Environmental Engineering, National University of Sciences and Technology, Sector H-12, Islamabad, PakistanNUST Institute of Civil Engineering, School of Civil and Environmental Engineering, National University of Sciences and Technology, Sector H-12, Islamabad, PakistanSelective harvesting plays an important role on the dynamics of predator-prey interaction. On the other hand, the effect of predator self-limitation contributes remarkably to the stabilization of exploitative interactions. Keeping in view the selective harvesting and predator self-limitation, a discrete-time predator-prey model is discussed. Existence of fixed points and their local dynamics is explored for the proposed discrete-time model. Explicit principles of Neimark–Sacker bifurcation and period-doubling bifurcation are used for discussion related to bifurcation analysis in the discrete-time predator-prey system. The control of chaotic behavior is discussed with the help of methods related to state feedback control and parameter perturbation. At the end, some numerical examples are presented for verification and illustration of theoretical findings.http://dx.doi.org/10.1155/2020/6737098
collection DOAJ
language English
format Article
sources DOAJ
author Zhihua Chen
Qamar Din
Muhammad Rafaqat
Umer Saeed
Muhammad Bilal Ajaz
spellingShingle Zhihua Chen
Qamar Din
Muhammad Rafaqat
Umer Saeed
Muhammad Bilal Ajaz
Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation
Journal of Mathematics
author_facet Zhihua Chen
Qamar Din
Muhammad Rafaqat
Umer Saeed
Muhammad Bilal Ajaz
author_sort Zhihua Chen
title Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation
title_short Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation
title_full Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation
title_fullStr Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation
title_full_unstemmed Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation
title_sort discrete-time predator-prey interaction with selective harvesting and predator self-limitation
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2020-01-01
description Selective harvesting plays an important role on the dynamics of predator-prey interaction. On the other hand, the effect of predator self-limitation contributes remarkably to the stabilization of exploitative interactions. Keeping in view the selective harvesting and predator self-limitation, a discrete-time predator-prey model is discussed. Existence of fixed points and their local dynamics is explored for the proposed discrete-time model. Explicit principles of Neimark–Sacker bifurcation and period-doubling bifurcation are used for discussion related to bifurcation analysis in the discrete-time predator-prey system. The control of chaotic behavior is discussed with the help of methods related to state feedback control and parameter perturbation. At the end, some numerical examples are presented for verification and illustration of theoretical findings.
url http://dx.doi.org/10.1155/2020/6737098
work_keys_str_mv AT zhihuachen discretetimepredatorpreyinteractionwithselectiveharvestingandpredatorselflimitation
AT qamardin discretetimepredatorpreyinteractionwithselectiveharvestingandpredatorselflimitation
AT muhammadrafaqat discretetimepredatorpreyinteractionwithselectiveharvestingandpredatorselflimitation
AT umersaeed discretetimepredatorpreyinteractionwithselectiveharvestingandpredatorselflimitation
AT muhammadbilalajaz discretetimepredatorpreyinteractionwithselectiveharvestingandpredatorselflimitation
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