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A differential interaction scheme with tunable confidence ranges in opinion consensus: from integer order to fractional order

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  • Kecai Cao
  • YangQuan Chen
  • Juping Gu

Abstract

This paper proposes a novel differential interaction scheme to address the consensus problem in opinion dynamics. In this framework, state-dependent interactions – characterised by both full and bounded confidence ranges – are incorporated into the design of consensus protocols without introducing any discontinuities. Based on this scheme, sufficient conditions involving initial distribution and confidence ranges are derived to determine whether the system reaches consensus or undergoes fragmentation. By explicitly modelling individual memory effects via fractional-order dynamics and capturing the influence of neighbouring agents through varying confidence ranges, the proposed approach provides a unified framework for both integer-order and fractional-order opinion models. Simulation results are provided to illustrate the intricate interplay between individual memory and confidence ranges, demonstrating the flexibility and effectiveness of the proposed framework.

Suggested Citation

  • Kecai Cao & YangQuan Chen & Juping Gu, 2026. "A differential interaction scheme with tunable confidence ranges in opinion consensus: from integer order to fractional order," International Journal of Systems Science, Taylor & Francis Journals, vol. 57(5), pages 1401-1415, April.
    • Handle: RePEc:taf:tsysxx:v:57:y:2026:i:5:p:1401-1415
    DOI: 10.1080/00207721.2025.2530191
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