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Dynamics of generalized asynchronous Boolean networks based on probability transition: Searching for attractors and basins

Author

Listed:
  • Li, G.
  • Luo, C.
  • Zhou, S.
  • Xu, L.
  • Yan, P.
  • Zhang, H.

Abstract

This paper investigates the dynamics of generalized asynchronous Boolean networks based on probability transition, particularly the evolutionary trends of attractor and its basin. Specifically, first, the algebraic state space representation method converts the discrete network into a linear form to obtain the network transition matrix. Then, based on the generalized asynchronous update mechanism, a generalized probabilistic asynchronous Boolean network is constructed using the probabilistic transition method, and the probabilistic network transition matrix is obtained. Second, a necessary and sufficient condition is provided to convert the generalized probabilistic asynchronous Boolean network to an approximately deterministic system. Next, some necessary and sufficient conditions for the asymptotic fixed points and limit cycles are provided. Besides, the basins of the asymptotic fixed points and limit cycles are found and the state transition graph is drawn. Finally, two numerical examples verify the effectiveness of the proposed theorems.

Suggested Citation

  • Li, G. & Luo, C. & Zhou, S. & Xu, L. & Yan, P. & Zhang, H., 2025. "Dynamics of generalized asynchronous Boolean networks based on probability transition: Searching for attractors and basins," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:chsofr:v:197:y:2025:i:c:s0960077925004801
    DOI: 10.1016/j.chaos.2025.116467
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    References listed on IDEAS

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    1. Chao Luo & Xingyuan Wang, 2013. "Dynamics of Random Boolean Networks under Fully Asynchronous Stochastic Update Based on Linear Representation," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-12, June.
    2. Yue, Xiaole & Lv, Ge & Zhang, Ying, 2021. "Rare and hidden attractors in a periodically forced Duffing system with absolute nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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    6. Liangdong Hu & Limin Wang, 2013. "Using Consensus Bayesian Network to Model the Reactive Oxygen Species Regulatory Pathway," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-9, February.
    7. Lunshi Xu & Hao Zhang & Jianquan Lu & Chuan Zhang & Xianghui Su & Sultan M. Alghamdi, 2025. "Synchronization and stability for asynchronous temporal Boolean networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 36(03), pages 1-17, March.
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