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

G. Li, C. Luo, S. Zhou, L. Xu, P. Yan and H. Zhang

Chaos, Solitons & Fractals, 2025, vol. 197, issue C

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.

Keywords: Generalized asynchronous Boolean networks; Probability transition; Attractors; Basins (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:197:y:2025:i:c:s0960077925004801

DOI: 10.1016/j.chaos.2025.116467

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