IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v110y2018icp178-184.html
   My bibliography  Save this article

Uncertain impulsive Lotka–Volterra competitive systems: Robust stability of almost periodic solutions

Author

Listed:
  • Stamov, Gani Tr.
  • Simeonov, Stanislav
  • Stamova, Ivanka M.

Abstract

Models with uncertain values of their parameters are of a practical significance in different fields of science and technology. Uncertainty in the competitive models can greatly affect their dynamical behavior and, therefore, the analysis of the effects of uncertain terms in such models is very important in both theory and application. In this paper, we extend the existing N-species impulsive competitive models to the uncertainty case. The existence of a unique strictly positive and robustly exponentially stable almost periodic solution is investigated for the model. The main results are obtained by using Lyapunov-type functions and a comparison principle.

Suggested Citation

  • Stamov, Gani Tr. & Simeonov, Stanislav & Stamova, Ivanka M., 2018. "Uncertain impulsive Lotka–Volterra competitive systems: Robust stability of almost periodic solutions," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 178-184.
    • Handle: RePEc:eee:chsofr:v:110:y:2018:i:c:p:178-184
    DOI: 10.1016/j.chaos.2018.03.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918301127
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.03.017?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. Li, Dong & Wang, Shilong & Zhang, Xiaohong & Yang, Dan, 2009. "Impulsive control of uncertain Lotka–Volterra predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1572-1577.
    2. Mangiarotti, Sylvain & Le Jean, Flavie & Huc, Mireille & Letellier, Christophe, 2016. "Global modeling of aggregated and associated chaotic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 82-96.
    3. Liu, Bing & Teng, Zhidong & Liu, Wanbo, 2007. "Dynamic behaviors of the periodic Lotka–Volterra competing system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 356-370.
    4. Chen, Yanguang, 2012. "Fractal dimension evolution and spatial replacement dynamics of urban growth," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 115-124.
    5. Chen, Yanguang, 2009. "Spatial interaction creates period-doubling bifurcation and chaos of urbanization," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1316-1325.
    6. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2008. "Chaotic behavior of a Watt-type predator–prey system with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 706-718.
    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. Li, Mingyue & Chen, Huanzhen & Li, Xiaodi, 2021. "Exponential stability of nonlinear systems involving partial unmeasurable states via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Anatoliy Martynyuk & Gani Stamov & Ivanka Stamova & Ekaterina Gospodinova, 2023. "Formulation of Impulsive Ecological Systems Using the Conformable Calculus Approach: Qualitative Analysis," Mathematics, MDPI, vol. 11(10), pages 1-15, May.
    3. Fu, Chao & Zheng, Zhaoli & Zhu, Weidong & Lu, Kuan & Yang, Yongfeng, 2022. "Non-intrusive frequency response analysis of nonlinear systems with interval uncertainty: A comparative study," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

    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. Chen, Yanguang, 2014. "An allometric scaling relation based on logistic growth of cities," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 65-77.
    2. Chen, Yanguang, 2014. "Urban chaos and replacement dynamics in nature and society," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 373-384.
    3. Li, Dong & Wang, Shilong & Zhang, Xiaohong & Yang, Dan, 2009. "Impulsive control of uncertain Lotka–Volterra predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1572-1577.
    4. Chen, Yanguang & Huang, Linshan, 2019. "Modeling growth curve of fractal dimension of urban form of Beijing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1038-1056.
    5. Lü Ye & Yanguang Chen & Yuqing Long, 2023. "Exploring the Relationship between Urbanization and Ikization," Sustainability, MDPI, vol. 15(12), pages 1-17, June.
    6. Chen, Yanguang, 2020. "Equivalent relation between normalized spatial entropy and fractal dimension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    7. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2009. "Dynamics of a periodic Watt-type predator–prey system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1270-1282.
    8. Man, Wang & Nie, Qin & Li, Zongmei & Li, Hui & Wu, Xuewen, 2019. "Using fractals and multifractals to characterize the spatiotemporal pattern of impervious surfaces in a coastal city: Xiamen, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 44-53.
    9. Tian, Yuan & Gao, Yan & Sun, Kaibiao, 2022. "Global dynamics analysis of instantaneous harvest fishery model guided by weighted escapement strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    10. Wang, Xiaoqin & Wang, Weiming & Lin, Yezhi & Lin, Xiaolin, 2009. "The dynamical complexity of an impulsive Watt-type prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 731-744.
    11. Haidong Liu & Fanwei Meng, 2015. "Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-12, February.
    12. Chen, Yanguang, 2013. "Fractal analytical approach of urban form based on spatial correlation function," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 47-60.
    13. Doménech-Carbó, Antonio & Doménech-Casasús, Clara, 2021. "The evolution of COVID-19: A discontinuous approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    14. Doménech-Carbó, Antonio, 2019. "Rise and fall of historic tram networks: Logistic approximation and discontinuous events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 315-323.
    15. Jiao, Jianjun & Meng, Xinzhu & Chen, Lansun, 2009. "Harvesting policy for a delayed stage-structured Holling II predator–prey model with impulsive stocking prey," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 103-112.
    16. Chen, Yanguang & Feng, Jian, 2012. "Fractal-based exponential distribution of urban density and self-affine fractal forms of cities," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1404-1416.
    17. Chen, Yanguang, 2012. "Fractal dimension evolution and spatial replacement dynamics of urban growth," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 115-124.
    18. Dong, Zhengbin & Wu, Wenjie, 2015. "Exploring the geography of China's airport networks: a hybrid complex-network approach," LSE Research Online Documents on Economics 64508, London School of Economics and Political Science, LSE Library.
    19. Chen, Yanguang & Feng, Jian, 2017. "Spatial analysis of cities using Renyi entropy and fractal parameters," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 279-287.
    20. Lei Gong & Jianzhu Yang & Chong Wu & Hui Zhou, 2023. "Fractal Characteristics of the Spatial Texture in Traditional Miao Villages in Qiandongnan, Guizhou, China," Sustainability, MDPI, vol. 15(17), pages 1-23, September.

    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:110:y:2018:i:c:p:178-184. 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.