IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v626y2023ics0378437123006209.html
   My bibliography  Save this article

The impact of memory effect on time-delay logistic systems driven by a class of non-Gaussian noise

Author

Listed:
  • Wang, Qiubao
  • Hu, Zhouyu
  • Yang, Yanling
  • Zhang, Congqing
  • Han, Zikun

Abstract

This paper investigates the effects of different memory effects on the evolution of species population densities. A stochastic logistic model driven by non-Gaussian noise, with discrete and distributed time-delay, is considered. Taking memory intensity as a parameter, we investigated the evolution of population dynamics. In order to reduce the stochastic time delay equation to the average Itoˆ equation during its derivation, we adopted the stochastic averaging method and the generalized central manifold theory. It is used to capture the one-dimensional slow variables of a system near the critical state of the transition between two steady states during the evolution of the system. With the help of the one-dimensional Itoˆ equation governed by this slow variable, we perform dynamic analysis of the population progression. The results show a change in the population system from a single steady-state to a bi-periodic oscillation to a single steady-state again as memory intensity increased from weak to strong. Finally, numerical simulation verifies the rationality of the theoretical results. This general approach used in our research can also be extended to other fields for the study of similar problems, such as the analysis of the dynamics in network congestion control models.

Suggested Citation

  • Wang, Qiubao & Hu, Zhouyu & Yang, Yanling & Zhang, Congqing & Han, Zikun, 2023. "The impact of memory effect on time-delay logistic systems driven by a class of non-Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    • Handle: RePEc:eee:phsmap:v:626:y:2023:i:c:s0378437123006209
    DOI: 10.1016/j.physa.2023.129065
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123006209
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2023.129065?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. Caihong Wang & Jian Xu, 2010. "Effects of Time Delay and Noise on Asymptotic Stability in Human Quiet Standing Model," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-14, October.
    2. Pelinovsky, Efim & Kurkin, Andrey & Kurkina, Oxana & Kokoulina, Maria & Epifanova, Anastasia, 2020. "Logistic equation and COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Li, Kai & Wei, Junjie, 2009. "Stability and Hopf bifurcation analysis of a prey–predator system with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2606-2613.
    4. Li, Zhong & Han, Maoan & Chen, Fengde, 2014. "Almost periodic solutions of a discrete almost periodic logistic equation with delay," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 743-751.
    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. Dubey, Balram & Sajan, & Kumar, Ankit, 2021. "Stability switching and chaos in a multiple delayed prey–predator model with fear effect and anti-predator behavior," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 164-192.
    2. Perrier, Frédéric & Girault, Frédéric, 2022. "Scaling and fine structure of superstable periodic orbits in the logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    3. Calatayud, Julia & Jornet, Marc & Mateu, Jorge & Pinto, Carla M.A., 2023. "A new population model for urban infestations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. He, Xue-Zhong & Li, Kai, 2015. "Profitability of time series momentum," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 140-157.
    5. Karaoglu, Esra & Merdan, Huseyin, 2014. "Hopf bifurcations of a ratio-dependent predator–prey model involving two discrete maturation time delays," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 159-168.
    6. Pelinovsky, E. & Kokoulina, M. & Epifanova, A. & Kurkin, A. & Kurkina, O. & Tang, M. & Macau, E. & Kirillin, M., 2022. "Gompertz model in COVID-19 spreading simulation," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    7. De Cesare, Luigi & Sportelli, Mario, 2022. "A non-linear approach to Kalecki’s investment cycle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 57-70.
    8. Wang, Jingnan & Shi, Hongbin & Xu, Li & Zang, Lu, 2022. "Hopf bifurcation and chaos of tumor-Lymphatic model with two time delays," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    9. Akio Matsumoto & Ferenc Szidarovszky & Hiroyuki Yoshida, 2011. "Dynamics in Linear Cournot Duopolies with Two Time Delays," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 311-327, October.
    10. Sportelli, Mario & De Cesare, Luigi, 2019. "Fiscal policy delays and the classical growth cycle," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 9-31.
    11. Wang, Luxuan & Niu, Ben & Wei, Junjie, 2016. "Dynamical analysis for a model of asset prices with two delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 297-313.
    12. Qingsong Liu & Yiping Lin & Jingnan Cao & Jinde Cao, 2014. "Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-7, March.
    13. Son, Woo-Sik & Park, Young-Jai, 2011. "Delayed feedback on the dynamical model of a financial system," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 208-217.
    14. Hommes, Cars & Li, Kai & Wagener, Florian, 2022. "Production delays and price dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 194(C), pages 341-362.
    15. Sun, Li & Zhu, Haitao & Ding, Yanhui, 2020. "Impulsive control for persistence and periodicity of logistic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 294-305.
    16. De Cesare, Luigi & Sportelli, Mario, 2012. "Fiscal policy lags and income adjustment processes," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 433-438.
    17. Gökçe, Aytül & Yazar, Samire & Sekerci, Yadigar, 2022. "Stability of spatial patterns in a diffusive oxygen–plankton model with time lag effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 109-123.
    18. De Cesare, Luigi & Sportelli, Mario, 2020. "Stability and direction of Hopf bifurcations of a cyclical growth model with two-time delays and one-delay dependent coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    19. Otunuga, Olusegun Michael, 2021. "Time-dependent probability distribution for number of infection in a stochastic SIS model: case study COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    20. Paul, Ayan & Reja, Selim & Kundu, Sayani & Bhattacharya, Sabyasachi, 2021. "COVID-19 pandemic models revisited with a new proposal: Plenty of epidemiological models outcast the simple population dynamics solution," Chaos, Solitons & Fractals, Elsevier, vol. 144(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:phsmap:v:626:y:2023:i:c:s0378437123006209. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.