Bifurcation Analysis and Chaos Control of a Discrete Fractional-Order Modified Leslie–Gower Model with Nonlinear Harvesting Effects
This paper investigates the dynamical behavior of a discrete fractional-order modified Leslie–Gower model with a Michaelis–Menten-type harvesting mechanism and a Holling-II functional response. We analyze the existence and stability of the nonnegative equilibrium points. For the interior equilibrium...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/8/12/744 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846104578061238272 |
|---|---|
| author | Yao Shi Xiaozhen Liu Zhenyu Wang |
| author_facet | Yao Shi Xiaozhen Liu Zhenyu Wang |
| author_sort | Yao Shi |
| collection | DOAJ |
| description | This paper investigates the dynamical behavior of a discrete fractional-order modified Leslie–Gower model with a Michaelis–Menten-type harvesting mechanism and a Holling-II functional response. We analyze the existence and stability of the nonnegative equilibrium points. For the interior equilibrium points, we study the conditions for period-doubling and Neimark–Sacker bifurcations using the center manifold theorem and bifurcation theory. To control the chaos arising from these bifurcations, two chaos control strategies are proposed. Numerical simulations are performed to validate the theoretical results. The findings provide valuable insights into the sustainable management and conservation of ecological systems. |
| format | Article |
| id | doaj-art-803b2a38c9ef40259029e86e88f06e9e |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-803b2a38c9ef40259029e86e88f06e9e2024-12-27T14:27:10ZengMDPI AGFractal and Fractional2504-31102024-12-0181274410.3390/fractalfract8120744Bifurcation Analysis and Chaos Control of a Discrete Fractional-Order Modified Leslie–Gower Model with Nonlinear Harvesting EffectsYao Shi0Xiaozhen Liu1Zhenyu Wang2School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, ChinaSchool of Mathematics and Statistics, Shandong University Weihai, Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology Weihai, Weihai 264209, ChinaThis paper investigates the dynamical behavior of a discrete fractional-order modified Leslie–Gower model with a Michaelis–Menten-type harvesting mechanism and a Holling-II functional response. We analyze the existence and stability of the nonnegative equilibrium points. For the interior equilibrium points, we study the conditions for period-doubling and Neimark–Sacker bifurcations using the center manifold theorem and bifurcation theory. To control the chaos arising from these bifurcations, two chaos control strategies are proposed. Numerical simulations are performed to validate the theoretical results. The findings provide valuable insights into the sustainable management and conservation of ecological systems.https://www.mdpi.com/2504-3110/8/12/744discrete fractional modified Leslie–Gower modelbifurcationMichaelis–Menten-type harvestingpiecewise-constant argument methodchaos control |
| spellingShingle | Yao Shi Xiaozhen Liu Zhenyu Wang Bifurcation Analysis and Chaos Control of a Discrete Fractional-Order Modified Leslie–Gower Model with Nonlinear Harvesting Effects Fractal and Fractional discrete fractional modified Leslie–Gower model bifurcation Michaelis–Menten-type harvesting piecewise-constant argument method chaos control |
| title | Bifurcation Analysis and Chaos Control of a Discrete Fractional-Order Modified Leslie–Gower Model with Nonlinear Harvesting Effects |
| title_full | Bifurcation Analysis and Chaos Control of a Discrete Fractional-Order Modified Leslie–Gower Model with Nonlinear Harvesting Effects |
| title_fullStr | Bifurcation Analysis and Chaos Control of a Discrete Fractional-Order Modified Leslie–Gower Model with Nonlinear Harvesting Effects |
| title_full_unstemmed | Bifurcation Analysis and Chaos Control of a Discrete Fractional-Order Modified Leslie–Gower Model with Nonlinear Harvesting Effects |
| title_short | Bifurcation Analysis and Chaos Control of a Discrete Fractional-Order Modified Leslie–Gower Model with Nonlinear Harvesting Effects |
| title_sort | bifurcation analysis and chaos control of a discrete fractional order modified leslie gower model with nonlinear harvesting effects |
| topic | discrete fractional modified Leslie–Gower model bifurcation Michaelis–Menten-type harvesting piecewise-constant argument method chaos control |
| url | https://www.mdpi.com/2504-3110/8/12/744 |
| work_keys_str_mv | AT yaoshi bifurcationanalysisandchaoscontrolofadiscretefractionalordermodifiedlesliegowermodelwithnonlinearharvestingeffects AT xiaozhenliu bifurcationanalysisandchaoscontrolofadiscretefractionalordermodifiedlesliegowermodelwithnonlinearharvestingeffects AT zhenyuwang bifurcationanalysisandchaoscontrolofadiscretefractionalordermodifiedlesliegowermodelwithnonlinearharvestingeffects |