IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v150y2021ics0960077921004902.html
   My bibliography  Save this article

On detecting chaos in a prey-predator model with prey’s counter-attack on juvenile predators

Author

Listed:
  • Ghanbari, Behzad

Abstract

Chaotic nonlinear systems are systems whose main feature is extreme sensitivity to noise in the problem or the corresponding initial conditions. In this paper, we examine the chaotic nature of a biological system involving a differential operator based on exponential kernel law, namely the Caputo-Fabrizio derivative. To approximate the solutions of the system, an implicit algorithm using the product-integration rule and two-point Lagrange interpolation is adopted. Some basic properties of the model, including the equilibrium points and their stability analysis, are discussed. Also, we used two well-known tools to detect chaos, including smaller alignment index (SALI), and the 0-1 test. Through considering different choices of parameters in the model, several meaningful numerical simulations and chaos analysis are presented. By observing the results obtained in both tests for detecting chaos, it is clear that the predicted behaviors are completely consistent with the approximate results obtained for the system solutions.It is found that hiring a new derivative operator dramatically increases the reliability of the biological system in predicting different scenarios in real situations.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004902
    DOI: 10.1016/j.chaos.2021.111136
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921004902
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111136?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gao, Fei & Li, Xiling & Li, Wenqin & Zhou, Xianjin, 2021. "Stability analysis of a fractional-order novel hepatitis B virus model with immune delay based on Caputo-Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "A SIR model assumption for the spread of COVID-19 in different communities," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. 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.
    4. Barrio, Roberto, 2005. "Sensitivity tools vs. Poincaré sections," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 711-726.
    5. Kaushik, Rajat & Banerjee, Sandip, 2021. "Predator-prey system: Prey’s counter-attack on juvenile predators shows opposite side of the same ecological coin," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    6. Verma, Pratibha & Kumar, Manoj, 2021. "Analysis of a novel coronavirus (2019-nCOV) system with variable Caputo-Fabrizio fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    8. Panwar, Virender Singh & Sheik Uduman, P.S. & Gómez-Aguilar, J.F., 2021. "Mathematical modeling of coronavirus disease COVID-19 dynamics using CF and ABC non-singular fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    Full references (including those not matched with items on IDEAS)

    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. Omame, Andrew & Abbas, Mujahid & Abdel-Aty, Abdel-Haleem, 2022. "Assessing the impact of SARS-CoV-2 infection on the dynamics of dengue and HIV via fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Kumar, Sunil & Chauhan, R.P. & Momani, Shaher & Hadid, Samir, 2021. "A study of fractional TB model due to mycobacterium tuberculosis bacteria," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    3. Kritika, & Agarwal, Ritu & Purohit, Sunil Dutt, 2020. "Mathematical model for anomalous subdiffusion using comformable operator," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Mohamed M. Mousa & Fahad Alsharari, 2021. "A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases," Mathematics, MDPI, vol. 9(22), pages 1-12, November.
    5. 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.
    6. Ullah, Ihsan & Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "Investigation of fractional order tuberculosis (TB) model via Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. 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).
    8. Talal Daghriri & Michael Proctor & Sarah Matthews, 2022. "Evolution of Select Epidemiological Modeling and the Rise of Population Sentiment Analysis: A Literature Review and COVID-19 Sentiment Illustration," IJERPH, MDPI, vol. 19(6), pages 1-20, March.
    9. 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).
    10. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    11. 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).
    12. Hussain, Ghulam & Khan, Amir & Zahri, Mostafa & Zaman, Gul, 2022. "Ergodic stationary distribution of stochastic epidemic model for HBV with double saturated incidence rates and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    13. Khan, Hasib & Ibrahim, Muhammad & Abdel-Aty, Abdel-Haleem & Khashan, M. Motawi & Khan, Farhat Ali & Khan, Aziz, 2021. "A fractional order Covid-19 epidemic model with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    14. Hoang, Manh Tuan, 2022. "Reliable approximations for a hepatitis B virus model by nonstandard numerical schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 32-56.
    15. Alam, Mehboob & Zada, Akbar, 2022. "Implementation of q-calculus on q-integro-differential equation involving anti-periodic boundary conditions with three criteria," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    16. Lin William Cong & Ke Tang & Bing Wang & Jingyuan Wang, 2021. "An AI-assisted Economic Model of Endogenous Mobility and Infectious Diseases: The Case of COVID-19 in the United States," Papers 2109.10009, arXiv.org.
    17. Liaqat, Muhammad Imran & Akgül, Ali, 2022. "A novel approach for solving linear and nonlinear time-fractional Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    18. Yahya Almalki & Waqar Afzal, 2023. "Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr - h -Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    19. Hari Mohan Srivastava & Khaled M. Saad, 2020. "A Comparative Study of the Fractional-Order Clock Chemical Model," Mathematics, MDPI, vol. 8(9), pages 1-14, August.
    20. Wan, Jinming & Ichinose, Genki & Small, Michael & Sayama, Hiroki & Moreno, Yamir & Cheng, Changqing, 2022. "Multilayer networks with higher-order interaction reveal the impact of collective behavior on epidemic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 164(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:eee:chsofr:v:150:y:2021:i:c:s0960077921004902. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.