IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i20p4367-d1264091.html
   My bibliography  Save this article

Bifurcation and Stability Analysis of a New Fractional-Order Prey–Predator Model with Fear Effects in Toxic Injections

Author

Listed:
  • Cuimin Liu

    (Yellow River Middle School, Dongying 257068, China
    These authors contributed equally to this work.)

  • Yonggang Chen

    (College of Science, China University of Petroleum, Qingdao 266580, China
    These authors contributed equally to this work.)

  • Yingbin Yu

    (Qingdao No. 66 High School of Shandong Province, Qingdao 266031, China)

  • Zhen Wang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

Abstract

This paper proposes a prey–predator model affected by fear effects and toxic substances. We used the Lipschitz condition to prove the uniqueness of the model solution and Laplace transform to prove the boundedness of the model solution. We used the fractional-order stability theorem to provide sufficient conditions for the local stability of equilibrium points, and selected fractional-order derivatives as parameters to perform Hopf bifurcation analysis on the system. Finally, the theoretical results are verified via numerical simulation. The results show that a value of α will affect the stability of the system and that the population size and the effect of toxic substances have a huge impact on the stability of the system.

Suggested Citation

  • Cuimin Liu & Yonggang Chen & Yingbin Yu & Zhen Wang, 2023. "Bifurcation and Stability Analysis of a New Fractional-Order Prey–Predator Model with Fear Effects in Toxic Injections," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4367-:d:1264091
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/20/4367/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/20/4367/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Das, Meghadri & Samanta, G.P., 2020. "A delayed fractional order food chain model with fear effect and prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 218-245.
    2. Wang, Zhen & Xie, Yingkang & Lu, Junwei & Li, Yuxia, 2019. "Stability and bifurcation of a delayed generalized fractional-order prey–predator model with interspecific competition," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 360-369.
    3. Barman, Dipesh & Roy, Jyotirmoy & Alrabaiah, Hussam & Panja, Prabir & Mondal, Sankar Prasad & Alam, Shariful, 2021. "Impact of predator incited fear and prey refuge in a fractional order prey predator model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yan Zhou & Zhuang Cui & Ruimei Li, 2024. "Complex Dynamics and PID Control Strategies for a Fractional Three-Population Model," Mathematics, MDPI, vol. 12(23), pages 1-22, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Ning & Yan, Mengting, 2022. "Bifurcation control of a delayed fractional-order prey-predator model with cannibalism and disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    2. Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Three-dimensional pattern dynamics of a fractional predator-prey model with cross-diffusion and herd behavior," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    3. Jianguang Zhu & Kai Li & Binbin Hao, 2019. "Image Restoration by Second-Order Total Generalized Variation and Wavelet Frame Regularization," Complexity, Hindawi, vol. 2019, pages 1-16, March.
    4. Wu, Tianyu & Huang, Xia & Chen, Xiangyong & Wang, Jing, 2020. "Sampled-data H∞ exponential synchronization for delayed semi-Markov jump CDNs: A looped-functional approach," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    5. Wang, Xinhe & Lu, Junwei & Wang, Zhen & Li, Yuxia, 2020. "Dynamics of discrete epidemic models on heterogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    6. Ma, Tingting & Meng, Xinzhu & Hayat, Tasawar & Hobiny, Aatef, 2021. "Stability analysis and optimal harvesting control of a cross-diffusion prey-predator system," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Ghanbari, Behzad, 2021. "On detecting chaos in a prey-predator model with prey’s counter-attack on juvenile predators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Meghadri Das & Guruprasad Samanta & Manuel De la Sen, 2022. "A Fractional Order Model to Study the Effectiveness of Government Measures and Public Behaviours in COVID-19 Pandemic," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    9. Zhang, Shuo & Liu, Lu & Xue, Dingyu, 2020. "Nyquist-based stability analysis of non-commensurate fractional-order delay systems," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    10. Juan Liu & Jie Hu & Peter Yuen & Fuzhong Li, 2022. "A Seasonally Competitive M-Prey and N-Predator Impulsive System Modeled by General Functional Response for Integrated Pest Management," Mathematics, MDPI, vol. 10(15), pages 1-15, July.
    11. Shuai Li & Chengdai Huang & Xinyu Song, 2019. "Bifurcation Based-Delay Feedback Control Strategy for a Fractional-Order Two-Prey One-Predator System," Complexity, Hindawi, vol. 2019, pages 1-13, April.
    12. Dai, Mingcheng & Huang, Zhengguo & Xia, Jianwei & Meng, Bo & Wang, Jian & Shen, Hao, 2019. "Non-fragile extended dissipativity-based state feedback control for 2-D Markov jump delayed systems," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    13. Barman, Dipesh & Roy, Jyotirmoy & Alam, Shariful, 2022. "Impact of wind in the dynamics of prey–predator interactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 49-81.
    14. Yang, Chengyu & Li, Fei & Kong, Qingkai & Chen, Xiangyong & Wang, Jian, 2021. "Asynchronous fault-tolerant control for stochastic jumping singularly perturbed systems: An H∞ sliding mode control scheme," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    15. He, Hua & Wang, Wendi, 2024. "Asymptotically periodic solutions of fractional order systems with applications to population models," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    16. Liang, Xingyue & Xia, Jianwei & Chen, Guoliang & Zhang, Huasheng & Wang, Zhen, 2019. "Dissipativity-based sampled-data control for fuzzy Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 552-564.
    17. Ghosh, Uttam & Pal, Swadesh & Banerjee, Malay, 2021. "Memory effect on Bazykin’s prey-predator model: Stability and bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    18. Zhang, Yan & Wang, Fang, 2019. "Adaptive neural control of non-strict feedback system with actuator failures and time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    19. Zhang, Hai & Cheng, Yuhong & Zhang, Weiwei & Zhang, Hongmei, 2023. "Time-dependent and Caputo derivative order-dependent quasi-uniform synchronization on fuzzy neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 846-857.
    20. Sajan, & Dubey, Balram & Sasmal, Sourav Kumar, 2022. "Chaotic dynamics of a plankton-fish system with fear and its carry over effects in the presence of a discrete delay," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4367-:d:1264091. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.