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Constructing bifurcation diagram of reservoir computing

Author

Listed:
  • Chen, Xiaolu
  • Weng, Tongfeng
  • Ren, Zhuoming
  • Yang, Huijie

Abstract

We introduce a data-driven synchronization approach to construct the dynamical transition of reservoir computing. Specifically, we design a scheme composed of three identically coupled reservoir computers and each of them has learned the underlying chaotic information of a considered system. After realizing synchronization among these reservoir computers, we find that the bifurcation diagram of reservoir computing can be fully constructed by varying the leaking rate. Numerical results on several chaotic systems have further confirmed the effectiveness of our method. Our findings provide a new perspective on studying the internal dynamics of reservoir computing, paving the way for further practical applications.

Suggested Citation

  • Chen, Xiaolu & Weng, Tongfeng & Ren, Zhuoming & Yang, Huijie, 2025. "Constructing bifurcation diagram of reservoir computing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 677(C).
    • Handle: RePEc:eee:phsmap:v:677:y:2025:i:c:s0378437125005667
    DOI: 10.1016/j.physa.2025.130914
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    References listed on IDEAS

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    1. Chen, Xiaolu & Weng, Tongfeng & Gu, Changgui & Yang, Huijie, 2019. "Synchronizing hyperchaotic subsystems with a single variable: A reservoir computing approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    2. Ghosh, Dibakar & Chowdhury, A. Roy & Saha, Papri, 2008. "Multiple delay Rössler system—Bifurcation and chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 472-485.
    3. Chen, Xiaolu & Weng, Tongfeng & Yang, Huijie, 2023. "Synchronization of spatiotemporal chaos and reservoir computing via scalar signals," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Ma, Rencai & Dai, Qionglin & Li, Haihong & Yang, Junzhong, 2023. "Dynamics reconstruction in the presence of bistability by using reservoir computer," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    5. Weng, Tongfeng & Chen, Xiaolu & Ren, Zhuoming & Yang, Huijie & Zhang, Jie & Small, Michael, 2023. "Synchronization of multiple mobile reservoir computing oscillators in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    6. Weng, Tongfeng & Song, Jia & Yang, Huijie & Gu, Changgui & Zhang, Jie & Small, Michael, 2020. "Synchronization of reservoir computers with applications to communications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    7. Marten Scheffer & Jordi Bascompte & William A. Brock & Victor Brovkin & Stephen R. Carpenter & Vasilis Dakos & Hermann Held & Egbert H. van Nes & Max Rietkerk & George Sugihara, 2009. "Early-warning signals for critical transitions," Nature, Nature, vol. 461(7260), pages 53-59, September.
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