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

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals Pub Date : 2025-04-29 DOI:10.1016/j.chaos.2025.116467

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

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引用次数: 0

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.

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基于概率转移的广义异步布尔网络动力学：寻找吸引子和盆地

本文研究了基于概率转移的广义异步布尔网络的动力学，特别是吸引子及其盆的演化趋势。具体而言，首先采用代数状态空间表示方法将离散网络转换成线性形式，得到网络转移矩阵。然后，基于广义异步更新机制，利用概率转移方法构造了广义概率异步布尔网络，得到了概率网络转移矩阵。其次，给出了将广义概率异步布尔网络转化为近似确定性系统的充分必要条件。其次，给出了渐近不动点和极限环存在的充分必要条件。此外，还找到了渐近不动点和极限环的域，并绘制了状态转移图。最后，通过两个算例验证了所提定理的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Chaos Solitons & Fractals 物理-数学跨学科应用

CiteScore

13.20

自引率

10.30%

发文量

1087

审稿时长

9 months

期刊介绍： Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.