Stability analysis of Boolean networks with Markov jump disturbances and their application in apoptosis networks

Hankang Ji; Yuanyuan Li; Xueying Ding; Jianquan Lu; Hankang Ji; Yuanyuan Li; Xueying Ding; Jianquan Lu

doi:10.3934/era.2022174

Electronic Research Archive

2022, Volume 30, Issue 9: 3422-3434. doi: 10.3934/era.2022174

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Stability analysis of Boolean networks with Markov jump disturbances and their application in apoptosis networks

1.
Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China
2.
School of Mathematics, Southeast University, Nanjing 210096, China

Academic Editor: Wei Lin

Received: 13 May 2022 Revised: 23 June 2022 Accepted: 28 June 2022 Published: 20 July 2022

In this paper, the finite-time stability (FTS) of switched Boolean networks (SBNs) with Markov jump disturbances under the conditions of arbitrary switching signals is studied. By using the tool of the semi-tensor product, the equivalent linear-like form of SBNs with Markov jump disturbances is first established. Next, to facilitate investigation, we convert the addressed system into an augmented Markov jump Boolean network (MJBN), and propose the definition of the switching set reachability of MJBNs. A necessary and sufficient criterion is developed for the FTS of SBNs with Markov jump disturbances under the conditions of arbitrary switching signals. Finally, we give two examples to illustrate the effectiveness of our work.
- Switched Boolean network,
- semi-tensor product,
- Markov jump disturbance,
- finite-time stability
Citation: Hankang Ji, Yuanyuan Li, Xueying Ding, Jianquan Lu. Stability analysis of Boolean networks with Markov jump disturbances and their application in apoptosis networks[J]. Electronic Research Archive, 2022, 30(9): 3422-3434. doi: 10.3934/era.2022174

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Abstract

In this paper, the finite-time stability (FTS) of switched Boolean networks (SBNs) with Markov jump disturbances under the conditions of arbitrary switching signals is studied. By using the tool of the semi-tensor product, the equivalent linear-like form of SBNs with Markov jump disturbances is first established. Next, to facilitate investigation, we convert the addressed system into an augmented Markov jump Boolean network (MJBN), and propose the definition of the switching set reachability of MJBNs. A necessary and sufficient criterion is developed for the FTS of SBNs with Markov jump disturbances under the conditions of arbitrary switching signals. Finally, we give two examples to illustrate the effectiveness of our work.

References

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