Abstract
We investigate the stability of Boolean networks (BNs) with impulses triggered by both states and random factors. A hybrid index model is used to describe impulsive BNs. First, several necessary and sufficient conditions for forward completeness are obtained. Second, based on the stability criterion of probabilistic BNs and the forward completeness criterion, the necessary and sufficient conditions for the finite-time stability with probability one and the asymptotical stability in distribution are presented. The relationship between these two kinds of stability is discussed. Last, examples and time-domain simulations are provided to illustrate the obtained results.
摘要
研究了具有由状态和随机因素触发脉冲的布尔网络的稳定性. 采用混合指数模型描述脉冲神经网络. 首先, 得到前向完备性的几个充要条件. 其次, 基于概率布尔网络的稳定性准则和前向完备性准则, 给出以概率1有限时间稳定性和依分布渐近稳定性的充要条件. 讨论了这两种稳定性之间的关系. 最后, 给出算例和时域仿真结果.
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Yu-qian GUO proposed the main idea. Ya-wen SHEN derived the main results and drafted the manuscript. Weihua GUI guided the research. Yu-qian GUO revised and finalized the paper.
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Ya-wen SHEN, Yu-qian GUO, and Wei-hua GUI declare that they have no conflict of interest.
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Project supported by the National Natural Science Foundation of China (Nos. 61873284, 61473315, and 61321003)
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Shen, Yw., Guo, Yq. & Gui, Wh. Stability of Boolean networks with state-dependent random impulses. Front Inform Technol Electron Eng 22, 222–231 (2021). https://doi.org/10.1631/FITEE.1900454
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DOI: https://doi.org/10.1631/FITEE.1900454
Key words
- Boolean network with impulses
- Forward completeness
- Finite-time stability with probability one
- Asymptotical stability in distribution