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

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  • 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.

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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.
    6. Chen, Yanguang, 2009. "Spatial interaction creates period-doubling bifurcation and chaos of urbanization," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1316-1325.
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    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).

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