IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i19p2468-d649264.html
   My bibliography  Save this article

Mathematical Problems of Managing the Risks of Complex Systems under Targeted Attacks with Known Structures

Author

Listed:
  • Alexander Shiroky

    (V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia)

  • Andrey Kalashnikov

    (V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia)

Abstract

This paper deals with the problem of managing the risks of complex systems under targeted attacks. It is usually solved by using Defender–Attacker models or similar ones. However, such models do not consider the influence of the defending system structure on the expected attack outcome. Our goal was to study how the structure of an abstract system affects its integral risk. To achieve this, we considered a situation where the Defender knows the structure of the expected attack and can arrange the elements to achieve a minimum of integral risk. In this paper, we consider a particular case of a simple chain attack structure. We generalized the concept of a local risk function to account for structural effects and found an ordering criterion that ensures the optimal placement of the defending system’s elements inside a given simple chain structure. The obtained result is the first step to formulate the principles of optimally placing system elements within an arbitrarily complex network. Knowledge of these principles, in turn, will allow solving the problems of optimal allocation of resources to minimize the risks of a complex system, considering its structure.

Suggested Citation

  • Alexander Shiroky & Andrey Kalashnikov, 2021. "Mathematical Problems of Managing the Risks of Complex Systems under Targeted Attacks with Known Structures," Mathematics, MDPI, vol. 9(19), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2468-:d:649264
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/19/2468/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/19/2468/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    2. Wang, Shuliang & Hong, Liu & Chen, Xueguang, 2012. "Vulnerability analysis of interdependent infrastructure systems: A methodological framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3323-3335.
    3. Cui, Pengshuai & Zhu, Peidong & Wang, Ke & Xun, Peng & Xia, Zhuoqun, 2018. "Enhancing robustness of interdependent network by adding connectivity and dependence links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 185-197.
    4. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
    5. Drossel, B. & Schwabl, F., 1993. "Forest-fire model with immune trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 199(2), pages 183-197.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Yapeng & Qiao, Shun & Deng, Ye & Wu, Jun, 2019. "Stackelberg game in critical infrastructures from a network science perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 705-714.
    2. Kashin Sugishita & Yasuo Asakura, 2021. "Vulnerability studies in the fields of transportation and complex networks: a citation network analysis," Public Transport, Springer, vol. 13(1), pages 1-34, March.
    3. Starita, Stefano & Scaparra, Maria Paola, 2016. "Optimizing dynamic investment decisions for railway systems protection," European Journal of Operational Research, Elsevier, vol. 248(2), pages 543-557.
    4. Alice Paul & Susan E. Martonosi, 2024. "The all-pairs vitality-maximization (VIMAX) problem," Annals of Operations Research, Springer, vol. 338(2), pages 1019-1048, July.
    5. Hongli Zhou & Mingxuan Yang, 2023. "Towards Evaluating the Robustness of the Open-Source Product Community under Multiple Attack Strategies," Sustainability, MDPI, vol. 15(17), pages 1-19, August.
    6. Wang, Weiping & Yang, Saini & Hu, Fuyu & Stanley, H. Eugene & He, Shuai & Shi, Mimi, 2018. "An approach for cascading effects within critical infrastructure systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 164-177.
    7. Kim, Dong Hwan & Eisenberg, Daniel A. & Chun, Yeong Han & Park, Jeryang, 2017. "Network topology and resilience analysis of South Korean power grid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 13-24.
    8. Lucas Cuadra & Sancho Salcedo-Sanz & Javier Del Ser & Silvia Jiménez-Fernández & Zong Woo Geem, 2015. "A Critical Review of Robustness in Power Grids Using Complex Networks Concepts," Energies, MDPI, vol. 8(9), pages 1-55, August.
    9. Alexander Veremyev & Konstantin Pavlikov & Eduardo L. Pasiliao & My T. Thai & Vladimir Boginski, 2019. "Critical nodes in interdependent networks with deterministic and probabilistic cascading failures," Journal of Global Optimization, Springer, vol. 74(4), pages 803-838, August.
    10. Faramondi, Luca & Setola, Roberto & Panzieri, Stefano & Pascucci, Federica & Oliva, Gabriele, 2018. "Finding critical nodes in infrastructure networks," International Journal of Critical Infrastructure Protection, Elsevier, vol. 20(C), pages 3-15.
    11. Marcus Engsig & Alejandro Tejedor & Yamir Moreno & Efi Foufoula-Georgiou & Chaouki Kasmi, 2024. "DomiRank Centrality reveals structural fragility of complex networks via node dominance," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    12. Ghorbani-Renani, Nafiseh & González, Andrés D. & Barker, Kash & Morshedlou, Nazanin, 2020. "Protection-interdiction-restoration: Tri-level optimization for enhancing interdependent network resilience," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    13. Zhang, Chi & Ramirez-Marquez, José Emmanuel & Wang, Jianhui, 2015. "Critical infrastructure protection using secrecy – A discrete simultaneous game," European Journal of Operational Research, Elsevier, vol. 242(1), pages 212-221.
    14. Wang, Zhuoyang & Chen, Guo & Hill, David J. & Dong, Zhao Yang, 2016. "A power flow based model for the analysis of vulnerability in power networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 105-115.
    15. Chan Y. Han & Brian J. Lunday & Matthew J. Robbins, 2016. "A Game Theoretic Model for the Optimal Location of Integrated Air Defense System Missile Batteries," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 405-416, August.
    16. Ryan M. Hynes & Bernardo S. Buarque & Ronald B. Davies & Dieter F. Kogler, 2020. "Hops, Skip & a Jump - The Regional Uniqueness of Beer Styles," Working Papers 202013, Geary Institute, University College Dublin.
    17. Lenore Newman & Ann Dale, 2007. "Homophily and Agency: Creating Effective Sustainable Development Networks," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 9(1), pages 79-90, February.
    18. Aybike Ulusan & Ozlem Ergun, 2018. "Restoration of services in disrupted infrastructure systems: A network science approach," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-28, February.
    19. David Simchi-Levi & Nikolaos Trichakis & Peter Yun Zhang, 2019. "Designing Response Supply Chain Against Bioattacks," Operations Research, INFORMS, vol. 67(5), pages 1246-1268, September.
    20. Yang, Hyeonchae & Jung, Woo-Sung, 2016. "Structural efficiency to manipulate public research institution networks," Technological Forecasting and Social Change, Elsevier, vol. 110(C), pages 21-32.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2468-:d:649264. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.