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Stability analysis of hybrid high-order nonlinear multiple time-delayed coupled systems via aperiodically intermittent control

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  • Han, Haoming
  • Zhang, Jing
  • Liu, Yan

Abstract

New results on the stability of hybrid high-order nonlinear multiple time-delayed coupled systems (HHNCSs) are presented by aperiodically intermittent control (AIC). The model considered in this paper includes Markovian switching and multiple time delays, which make the high-order nonlinear coupled systems more accurately simulate the actual models. In addition, Halanay-type differential inequalities are powerful tools when investigating the stability of time-delayed systems with AIC. However, existing Halanay-type differential inequalities are not applicable for HHNCSs, since high-order nonlinear terms exist. Therefore, a novel Halanay-type differential inequality is established which not only generalizes the classic Halanay inequality but also develops the applications of AIC under the condition of high-order nonlinearity. On the foundation of this innovative Halanay-type differential inequality, sufficient conditions are obtained by employing the graph theory and the Lyapunov method. Finally, the obtained theoretical results can be applied to modified coupled Van Pol–Duffing oscillators and some simulation results are given to demonstrate the feasibility and validity of our results.

Suggested Citation

  • Han, Haoming & Zhang, Jing & Liu, Yan, 2023. "Stability analysis of hybrid high-order nonlinear multiple time-delayed coupled systems via aperiodically intermittent control," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004629
    DOI: 10.1016/j.chaos.2023.113561
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    References listed on IDEAS

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    1. Khajanchi, Subhas & Nieto, Juan J., 2019. "Mathematical modeling of tumor-immune competitive system, considering the role of time delay," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 180-205.
    2. Khajanchi, Subhas, 2015. "Bifurcation analysis of a delayed mathematical model for tumor growth," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 264-276.
    3. Sardar, Mrinmoy & Biswas, Santosh & Khajanchi, Subhas, 2021. "The impact of distributed time delay in a tumor-immune interaction system," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Wiggers, Vinícius & Rech, Paulo C., 2017. "Multistability and organization of periodicity in a Van der Pol–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 632-637.
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