IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v682y2026ics0378437125007666.html

Competitiveness of competing complex systems

Author

Listed:
  • Li, Meixuan Jade
  • Zhu, Cheng
  • Zhu, Xianqiang
  • Tse, Chi K.

Abstract

This study presents a framework for analyzing the competitiveness of complex systems in competing processes, highlighting the interdependent dynamics of opposing systems and the internal topology of each system. We incorporate three key factors that shape system behavior: node heterogeneity, spatiotemporal competing strategies, and intra-system interaction patterns. Node heterogeneity includes variations in node parameters. Spatiotemporal engagement strategies arise from geographical distributions of nodes in a system that influence the engagement timing of nodes in opposing systems. Various interaction patterns influence resource consumption in complex systems. The proposed computational framework allows us to quantify how bidirectional attack-defense dependencies generate coupled vulnerability states of opposing systems. We find that prioritizing nodes with higher internal connectivity in the early stages of participation enhances the competitiveness of the system. Moreover, simulations show that Watts–Strogatz networks are less competitive than Erdős–Rényi random networks with comparable edge density.

Suggested Citation

  • Li, Meixuan Jade & Zhu, Cheng & Zhu, Xianqiang & Tse, Chi K., 2026. "Competitiveness of competing complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 682(C).
    • Handle: RePEc:eee:phsmap:v:682:y:2026:i:c:s0378437125007666
    DOI: 10.1016/j.physa.2025.131114
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437125007666
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2025.131114?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Jianxi Gao & Baruch Barzel & Albert-László Barabási, 2016. "Erratum: Universal resilience patterns in complex networks," Nature, Nature, vol. 536(7615), pages 238-238, August.
    2. Abhijit Chakraborty & Tobias Reisch & Christian Diem & Pablo Astudillo-Estévez & Stefan Thurner, 2024. "Inequality in economic shock exposures across the global firm-level supply network," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    3. Jianxi Gao & Baruch Barzel & Albert-László Barabási, 2016. "Universal resilience patterns in complex networks," Nature, Nature, vol. 530(7590), pages 307-312, February.
    4. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    5. Ash, J. & Newth, D., 2007. "Optimizing complex networks for resilience against cascading failure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 673-683.
    6. S. J. Deitchman, 1962. "A Lanchester Model of Guerrilla Warfare," Operations Research, INFORMS, vol. 10(6), pages 818-827, December.
    7. Moshe Kress, 2020. "Lanchester Models for Irregular Warfare," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    8. Anna D. Broido & Aaron Clauset, 2019. "Scale-free networks are rare," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    9. Peter J. Menck & Jobst Heitzig & Jürgen Kurths & Hans Joachim Schellnhuber, 2014. "How dead ends undermine power grid stability," Nature Communications, Nature, vol. 5(1), pages 1-8, September.
    10. Kress, Moshe & Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Seidl, Andrea, 2018. "Lanchester model for three-way combat," European Journal of Operational Research, Elsevier, vol. 264(1), pages 46-54.
    11. Tianlei Zhu & Xin Yang & Zhiao Ma & Huijun Sun & Jianjun Wu & Ziyou Gao & Jianxi Gao, 2025. "A small set of critical hyper-motifs governs heterogeneous flow-weighted network resilience," Nature Communications, Nature, vol. 16(1), pages 1-11, December.
    12. Chang Liu & Fengli Xu & Chen Gao & Zhaocheng Wang & Yong Li & Jianxi Gao, 2024. "Deep learning resilience inference for complex networked systems," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
    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. Tianlei Zhu & Xin Yang & Zhiao Ma & Huijun Sun & Jianjun Wu & Ziyou Gao & Jianxi Gao, 2025. "A small set of critical hyper-motifs governs heterogeneous flow-weighted network resilience," Nature Communications, Nature, vol. 16(1), pages 1-11, December.
    2. Gangwal, Utkarsh & Singh, Mayank & Pandey, Pradumn Kumar & Kamboj, Deepak & Chatterjee, Samrat & Bhatia, Udit, 2022. "Identifying early-warning indicators of onset of sudden collapse in networked infrastructure systems against sequential disruptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    3. Fu, Jun & Sun, Xiaojie & Zhang, Peng & Findeisen, Rolf, 2026. "Exploring diverse solutions in network dismantling with generative model," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    4. Meng, Xiangyi & Zhou, Bin, 2023. "Scale-free networks beyond power-law degree distribution," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    5. Aura Reggiani, 2022. "The Architecture of Connectivity: A Key to Network Vulnerability, Complexity and Resilience," Networks and Spatial Economics, Springer, vol. 22(3), pages 415-437, September.
    6. Cerqueti, Roy & Ferraro, Giovanna & Iovanella, Antonio, 2019. "Measuring network resilience through connection patterns," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 320-329.
    7. Wu, Chengxing & Duan, Dongli, 2024. "Collapse process prediction of mutualistic dynamical networks with k-core and dimension reduction method," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    8. Vikram Mittal, 2026. "Estimating attrition coefficients for the Lanchester equations from small-unit combat models," The Journal of Defense Modeling and Simulation, , vol. 23(2), pages 193-205, April.
    9. Chang Liu & Fengli Xu & Chen Gao & Zhaocheng Wang & Yong Li & Jianxi Gao, 2024. "Deep learning resilience inference for complex networked systems," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
    10. Wu, Min & Mou, Jianhong & Dai, Bitao & Tan, Suoyi & Lu, Xin, 2025. "Dismantling directed networks: A multi-temporal information field approach," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    11. Zhou, Xun & Dong, Gaogao & Wang, Fan & Du, Ruijin & Lambiotte, Renaud, 2025. "Repairing a failed clustered network by external activation," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    12. Xu, Peng-Cheng & Lu, Qing-Chang & Xie, Chi & Cheong, Taesu, 2024. "Modeling the resilience of interdependent networks: The role of function dependency in metro and bus systems," Transportation Research Part A: Policy and Practice, Elsevier, vol. 179(C).
    13. Lai, Keyuan & Zeng, An, 2025. "Targeted attack in spatial networks with minimal collateral damage," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    14. Lv, Changchun & Yuan, Ziwei & Si, Shubin & Duan, Dongli, 2021. "Robustness of scale-free networks with dynamical behavior against multi-node perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    15. Didier Wernli & Lucas Böttcher & Flore Vanackere & Yuliya Kaspiarovich & Maria Masood & Nicolas Levrat, 2023. "Understanding and governing global systemic crises in the 21st century: A complexity perspective," Global Policy, London School of Economics and Political Science, vol. 14(2), pages 207-228, May.
    16. Prasan Ratnayake & Sugandima Weragoda & Janaka Wansapura & Dharshana Kasthurirathna & Mahendra Piraveenan, 2021. "Quantifying the Robustness of Complex Networks with Heterogeneous Nodes," Mathematics, MDPI, vol. 9(21), pages 1-20, November.
    17. Roy Cerqueti & Matteo Cinelli & Giovanna Ferraro & Antonio Iovanella, 2023. "Financial interbanking networks resilience under shocks propagation," Annals of Operations Research, Springer, vol. 330(1), pages 389-409, November.
    18. Fabrizio Lillo & Giorgio Rizzini, 2024. "Modelling shock propagation and resilience in financial temporal networks," Papers 2407.09340, arXiv.org.
    19. 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.
    20. Lv, Changchun & Yuan, Ziwei & Si, Shubin & Duan, Dongli & Yao, Shirui, 2022. "Cascading failure in networks with dynamical behavior against multi-node removal," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:phsmap:v:682:y:2026:i:c:s0378437125007666. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.