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Dynamics of interdependent critical infrastructures – A mathematical model with unexpected results

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  • Klein, Peter
  • Klein, Fabian

Abstract

The article develops a formal mathematical model which describes the dynamic interactions of interdependent critical infrastructures in discrete time steps, i.e. the direct and indirect consequences (cascading effects) of a disrupted infrastructure to depending infrastructures. The main result here is that a disturbed infrastructure with only a reduced performance level draws (on the long run) all other infrastructures to the same reduced performance level. Also the development of all infrastructures after a full repair of the disturbances is investigated. The related result is that even after a full repair the infrastructures cannot return to full performance without external support. Both results are proved as mathematical theorems. Visualized examples are shown to demonstrate the results.

Suggested Citation

  • Klein, Peter & Klein, Fabian, 2019. "Dynamics of interdependent critical infrastructures – A mathematical model with unexpected results," International Journal of Critical Infrastructure Protection, Elsevier, vol. 24(C), pages 69-77.
    • Handle: RePEc:eee:ijocip:v:24:y:2019:i:c:p:69-77
    DOI: 10.1016/j.ijcip.2018.11.002
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    References listed on IDEAS

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