Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model
Bifurcation theory (center manifold and Ljapunov-Schmidt reduction, normal form theory, universal unfolding, calculation of bifurcation diagrams) has become an important and very useful means in the solution of nonlinear stability problems in many branches of engineering. The present study deals wit...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9138422/ |
| _version_ | 1819276637398630400 |
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| author | Youping Lin Qamar Din Muhammad Rafaqat Abdelalim A. Elsadany Yanqiu Zeng |
| author_facet | Youping Lin Qamar Din Muhammad Rafaqat Abdelalim A. Elsadany Yanqiu Zeng |
| author_sort | Youping Lin |
| collection | DOAJ |
| description | Bifurcation theory (center manifold and Ljapunov-Schmidt reduction, normal form theory, universal unfolding, calculation of bifurcation diagrams) has become an important and very useful means in the solution of nonlinear stability problems in many branches of engineering. The present study deals with qualitative behavior of a two-dimensional discrete-time system for interaction between prey and predator. The discrete-time model has more chaotic and rich dynamical behavior as compare to its continuous counterpart. We investigate the qualitative behavior of a discrete-time Lotka-Volterra model with linear functional response for prey. The local asymptotic behavior of equilibria is discussed for discrete-time Lotka-Volterra model. Furthermore, with the help of bifurcation theory and center manifold theorem, explicit parametric conditions for directions and existence of flip and Hopf bifurcations are investigated. Moreover, two chaos control methods, that is, OGY feedback control and hybrid control strategy, are implemented. Numerical simulations are provided to illustrate theoretical discussion and their effectiveness. |
| first_indexed | 2024-12-23T23:43:23Z |
| format | Article |
| id | doaj.art-a1e58b5ddc76461bbdaba204748000dc |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-23T23:43:23Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-a1e58b5ddc76461bbdaba204748000dc2022-12-21T17:25:35ZengIEEEIEEE Access2169-35362020-01-01812676012677510.1109/ACCESS.2020.30085229138422Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra ModelYouping Lin0https://orcid.org/0000-0001-8243-9612Qamar Din1https://orcid.org/0000-0002-0999-7404Muhammad Rafaqat2https://orcid.org/0000-0002-7437-5994Abdelalim A. Elsadany3https://orcid.org/0000-0001-5365-5316Yanqiu Zeng4https://orcid.org/0000-0003-4656-359XChengyi University College, Jimei University, Xiamen, ChinaDepartment of Mathematics, University of Poonch Rawalakot, Rawalakot, PakistanDepartment of Mathematics and Statistics, The University of Lahore, Lahore, PakistanDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi ArabiaChengyi University College, Jimei University, Xiamen, ChinaBifurcation theory (center manifold and Ljapunov-Schmidt reduction, normal form theory, universal unfolding, calculation of bifurcation diagrams) has become an important and very useful means in the solution of nonlinear stability problems in many branches of engineering. The present study deals with qualitative behavior of a two-dimensional discrete-time system for interaction between prey and predator. The discrete-time model has more chaotic and rich dynamical behavior as compare to its continuous counterpart. We investigate the qualitative behavior of a discrete-time Lotka-Volterra model with linear functional response for prey. The local asymptotic behavior of equilibria is discussed for discrete-time Lotka-Volterra model. Furthermore, with the help of bifurcation theory and center manifold theorem, explicit parametric conditions for directions and existence of flip and Hopf bifurcations are investigated. Moreover, two chaos control methods, that is, OGY feedback control and hybrid control strategy, are implemented. Numerical simulations are provided to illustrate theoretical discussion and their effectiveness.https://ieeexplore.ieee.org/document/9138422/Lotka-Volterra modelstabilityflip bifurcationHopf bifurcationchaos control |
| spellingShingle | Youping Lin Qamar Din Muhammad Rafaqat Abdelalim A. Elsadany Yanqiu Zeng Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model IEEE Access Lotka-Volterra model stability flip bifurcation Hopf bifurcation chaos control |
| title | Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model |
| title_full | Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model |
| title_fullStr | Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model |
| title_full_unstemmed | Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model |
| title_short | Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model |
| title_sort | dynamics and chaos control for a discrete time lotka volterra model |
| topic | Lotka-Volterra model stability flip bifurcation Hopf bifurcation chaos control |
| url | https://ieeexplore.ieee.org/document/9138422/ |
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