IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v152y2021ics0960077921006627.html
   My bibliography  Save this article

Dynamic analysis of a harvested fractional-order biological system with its discretization

Author

Listed:
  • Al-Nassir, Sadiq

Abstract

The complexity of nature that can not be modeled by means of ordinary or partial differential equations. This paper aims to study the dynamics behavior of fractional-order prey-predator system and its discretization with harvesting on prey species. The logistic growth of prey species and Holling type III functional response are considered. The existence and the local stability of all equilibria of fractional-order system, as well as its discretization, are determined and investigated. Then the discrete model is extended to an optimal control problem to get an optimal harvesting policy. We use the discrete version of Pontryagin maximum principle to derive the characterization of the optimal harvesting control and the optimal corresponding state solution. Numerical simulations are given to illustrate the theoretical findings.

Suggested Citation

  • Al-Nassir, Sadiq, 2021. "Dynamic analysis of a harvested fractional-order biological system with its discretization," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006627
    DOI: 10.1016/j.chaos.2021.111308
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921006627
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111308?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. Ortigueira, Manuel & Bengochea, Gabriel, 2017. "A new look at the fractionalization of the logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 554-561.
    2. Hoekstra, Jeljer & van den Bergh, Jeroen C.J.M., 2005. "Harvesting and conservation in a predator-prey system," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1097-1120, June.
    3. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    4. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    5. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
    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. Mehmood, Ammara & Raja, Muhammad Asif Zahoor, 2022. "Fuzzy-weighted differential evolution computing paradigm for fractional order nonlinear wiener systems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Li, Peiluan & Gao, Rong & Xu, Changjin & Li, Ying & Akgül, Ali & Baleanu, Dumitru, 2023. "Dynamics exploration for a fractional-order delayed zooplankton–phytoplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

    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. Antonio Rubia & Trino-Manuel Ñíguez, 2006. "Forecasting the conditional covariance matrix of a portfolio under long-run temporal dependence," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 439-458.
    2. Jonas Mockus, 2010. "On simulation of optimal strategies and Nash equilibrium in the financial market context," Journal of Global Optimization, Springer, vol. 48(1), pages 129-143, September.
    3. Claudio Morana, 2010. "Heteroskedastic Factor Vector Autoregressive Estimation of Persistent and Non Persistent Processes Subject to Structural Breaks," ICER Working Papers - Applied Mathematics Series 36-2010, ICER - International Centre for Economic Research.
    4. Claudio Morana, 2014. "Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks," Working Papers 273, University of Milano-Bicocca, Department of Economics, revised May 2014.
    5. Luis Gil-Alana, 2004. "Forecasting the real output using fractionally integrated techniques," Applied Economics, Taylor & Francis Journals, vol. 36(14), pages 1583-1589.
    6. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    7. Giorgio Canarella & Luis A. Gil-Alana & Rangan Gupta & Stephen M. Miller, 2022. "Globalization, long memory, and real interest rate convergence: a historical perspective," Empirical Economics, Springer, vol. 63(5), pages 2331-2355, November.
    8. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    9. Haldrup, Niels & Nielsen, Morten Orregaard, 2006. "A regime switching long memory model for electricity prices," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 349-376.
    10. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
    11. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2005. "Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study," Trinity Economics Papers tep20021, Trinity College Dublin, Department of Economics.
    12. El-Dessoky Ahmed, M.M. & Altaf Khan, Muhammad, 2020. "Modeling and analysis of the polluted lakes system with various fractional approaches," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    13. Geoffrey Ngene & Ann Nduati Mungai & Allen K. Lynch, 2018. "Long-Term Dependency Structure and Structural Breaks: Evidence from the U.S. Sector Returns and Volatility," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, June.
    14. Youwei Li & Xue-Zhong He, 2005. "Long Memory, Heterogeneity, and Trend Chasing," Computing in Economics and Finance 2005 113, Society for Computational Economics.
    15. Ra l De Jes s Guti rrez & Lidia E. Carvajal Guti rrez & Oswaldo Garcia Salgado, 2023. "Value at Risk and Expected Shortfall Estimation for Mexico s Isthmus Crude Oil Using Long-Memory GARCH-EVT Combined Approaches," International Journal of Energy Economics and Policy, Econjournals, vol. 13(4), pages 467-480, July.
    16. Karlis, Alexandros & Galanis, Girogos & Terovitis, Spyridon & Turner, Matthew, 2017. "Heterogeneity and Clustering of Defaults," Economic Research Papers 270011, University of Warwick - Department of Economics.
    17. Baillie, Richard T. & Kapetanios, George & Papailias, Fotis, 2014. "Bandwidth selection by cross-validation for forecasting long memory financial time series," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 129-143.
    18. Christos Christodoulou-Volos & Fotios Siokis, 2006. "Long range dependence in stock market returns," Applied Financial Economics, Taylor & Francis Journals, vol. 16(18), pages 1331-1338.
    19. Luis A. Gil-Alana & Antonio Moreno & Seonghoon Cho, 2012. "The Deaton paradox in a long memory context with structural breaks," Applied Economics, Taylor & Francis Journals, vol. 44(25), pages 3309-3322, September.
    20. Gadea, Maria Dolores & Sabate, Marcela & Serrano, Jose Maria, 2004. "Structural breaks and their trace in the memory: Inflation rate series in the long-run," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 14(2), pages 117-134, April.

    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:152:y:2021:i:c:s0960077921006627. 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.