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Polynomial Noises for Nonlinear Systems with Nonlinear Impulses and Time-Varying Delays

Author

Listed:
  • Lichao Feng

    (College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China)

  • Qiaona Wang

    (College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China)

  • Chunyan Zhang

    (College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China)

  • Dianxuan Gong

    (College of Science and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China)

Abstract

It is known that random noises have a significant impact on differential systems. Recently, the influences of random noises for impulsive systems have been started. Nevertheless, the existing references on this issue ignore the significant phenomena of nonlinear impulses and time-varying delays. Therefore, we see the necessity to study the influences of random noises for impulsive systems with the above two factors. Stimulated by the above, a polynomial random noise is introduced to suppress the potential explosive behavior of the nonlinear impulsive differential system with time-varying delay. Fortunately, the stochastically controlled impulsive delay differential system admits a unique global solution, is bounded, and grows at most in the polynomial form.

Suggested Citation

  • Lichao Feng & Qiaona Wang & Chunyan Zhang & Dianxuan Gong, 2022. "Polynomial Noises for Nonlinear Systems with Nonlinear Impulses and Time-Varying Delays," Mathematics, MDPI, vol. 10(9), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1525-:d:807587
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    References listed on IDEAS

    as
    1. Singh, Ajeet & Shukla, Anurag & Vijayakumar, V. & Udhayakumar, R., 2021. "Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Peng, Dongxue & Li, Xiaodi & Rakkiyappan, R. & Ding, Yanhui, 2021. "Stabilization of stochastic delayed systems: Event-triggered impulsive control," Applied Mathematics and Computation, Elsevier, vol. 401(C).
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    Cited by:

    1. Xinsong Yang & Ruofeng Rao, 2023. "Well-Posedness, Dynamics, and Control of Nonlinear Differential System with Initial-Boundary Value," Mathematics, MDPI, vol. 11(10), pages 1-4, May.

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