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On hybrid dynamical systems of differential–difference equations

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  • Dassios, Ioannis
  • Vaca, Angel
  • Milano, Federico

Abstract

In this paper, we define and study a class of linear hybrid dynamical systems characterized by differential–difference equations. We introduce two operators that facilitate the analysis of these systems and derive explicit formulas for their solutions. We examine the transfer function matrix and characteristic polynomial to assess stability. Our theoretical findings are supported by numerical examples, demonstrating their application in power systems stability analysis. Specifically, we substantiate our theory within the context of power systems stability analysis, incorporating elements of discrete behavior.

Suggested Citation

  • Dassios, Ioannis & Vaca, Angel & Milano, Federico, 2024. "On hybrid dynamical systems of differential–difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009834
    DOI: 10.1016/j.chaos.2024.115431
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    References listed on IDEAS

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    1. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & Elkhateeb S. Aly, 2023. "The Soliton Solutions of the Stochastic Shallow Water Wave Equations in the Sense of Beta-Derivative," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    2. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano, 2023. "On the Dynamical Behavior of Solitary Waves for Coupled Stochastic Korteweg–De Vries Equations," Mathematics, MDPI, vol. 11(16), pages 1-17, August.
    3. Dassios, Ioannis K. & Baleanu, Dumitru I., 2018. "Caputo and related fractional derivatives in singular systems," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 591-606.
    4. Dassios, Ioannis & Tzounas, Georgios & Milano, Federico, 2019. "The Möbius transform effect in singular systems of differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 338-353.
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