Skip to main content
SpringerLink
Log in

Set Stability of Probabilistic Time-Delay Boolean Networks with Impulsive Effect

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper investigates the set stability of probabilistic time-delay Boolean networks (PTDBN) with impulsive effect. Firstly, using the algebraic state space representation, an equivalent stochastic system is established for PTDBN with impulsive effect. Then, based on the probabilistic state transition matrix, a necessary and sufficient condition is presented for the set stability of PTDBN with impulsive effect. Finally, the obtained new result is applied to the networked evolutionary game with memories.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Li H T, Ding X Y, Alsaedi A, et al., Stochastic set stabilisation of n-person random evolutionary boolean games and its applications, IET Control Theory and Applications, 2017, 11(13): 2152–2160.

    Article  MathSciNet  Google Scholar 

  2. Guo P L, Zhang H X, Alsaadi F E, et al., Semi-tensor product method to a class of event-triggered control for finite evolutionary networked games, IET Control Theory and Applications, 2017, 11(13): 2140–2145.

    Article  MathSciNet  Google Scholar 

  3. Zhao G D, Wang Y Z, and Li H T, A matrix approach to the modeling and analysis of networked evolutionary games with time delays, IEEE-CAA Journal of Automatica Sinica, 2018, 5(4): 818–826.

    Article  MathSciNet  Google Scholar 

  4. Zaghrout A A S and Attalah S H, Analysis of a model of stage-structured populations dynamics growth with time state-dependent time delay, Applied Mathematics and Computation, 1996, 77(2–3): 185–194.

    Article  MathSciNet  Google Scholar 

  5. Misra A K, Mishra S N, Pathak A L, et al., A mathematical model for the control of carrier-depedent infectious diseases with direct transmission and time delay, Chaos, Solitons and Fractals, 2013, 57: 41–53.

    Article  MathSciNet  Google Scholar 

  6. Liu Y, Li B W, Chen H W, et al., Function perturbations on sigular boolean networks, Automatica, 2017, 84: 36–42.

    Article  Google Scholar 

  7. Zhang H, Wang X Y, and Lin X H, Synchronization of asynchronous switched boolean network, IEEE-ACM Transactions on Computational Biology and Bioinformatics, 2015, 12(6): 1449–1456.

    Article  Google Scholar 

  8. Revathi V M, Balasubramaniam P, and Ratnavelu K, Mode-dependent filtering for stochastic markovian switching genetic regulatory networks with leakage and time-varying delays, Circuits Systems and Signal Processing, 2014, 33(11): 3349–3388.

    Article  Google Scholar 

  9. Tian H, Zhang H G, Wang Z S, et al., Stabilization of fc-valued logical control networks by open-loop control via the reverse-transfer method, Automatica, 2017, 83: 387–390.

    Article  MathSciNet  Google Scholar 

  10. Chueh T H and Lu H H S, Inference of biological pathway from gene expression profiles by time delay boolean networks, Plos One, 2012, 7(8): e42095.

    Article  Google Scholar 

  11. Cotta C and Troya J M, Reverse engineering of temporal boolean networks from noisy data using evolutionary algorithms, Neurocomputing, 2004, 62: 111–129.

    Article  Google Scholar 

  12. Li Z Q and Song J L, Controllability of boolean control networks avoiding states set, Science China — Information Sciences, 2014, 57(3): 032205.

    MATH  Google Scholar 

  13. Li H T, Zheng Y T, and Alsaadi F E, Algebraic formulation and topological structure of boolean networks with state-dependent delay, Journal of Computational and Applied Mathematics, 2019, 350: 87–97.

    Article  MathSciNet  Google Scholar 

  14. Senthilkumar T and Balasubramaniam P, Non-fragile robust stabilization and H-infinity control for uncertain stochastic time delay systems with Markovian jump parameters and nonlinear disturbances, International Journal of Adaptive Control and Signal Processing, 2014, 28(3–5): 464–478.

    Article  MathSciNet  Google Scholar 

  15. Duemcke S, Braeuer J, Anchang B, et al., Exact likelihood computation in boolean networks with probabilistic time delays, and its application in signal network reconstruction, Bioinformatics, 2014, 30(3): 414–419.

    Article  Google Scholar 

  16. Li Y L, Li H T, and Wang S L, Finite-time consensus of finite field networks with stochastic time delays, IEEE Transactions on Circuits and Systems II: Express Briefs, 2020, 67(12): 3128–3132.

    Article  Google Scholar 

  17. Chaouki A and El Abed A, Finite-time and fixed-time synchronization of inertial neural networks with mixed delays, Journal of Systems Science and Complexity, 2021, 34(1): 206–235.

    Article  MathSciNet  Google Scholar 

  18. Cheng R R, Peng M S, Yu J C, et al., Synchronization for discrete-time complex networks with probabilistic time delays, Physica A: Statistical Mechanics and Its Applications, 2019, 525: 1088–1101.

    Article  MathSciNet  Google Scholar 

  19. Jiang D P and Zhang K Z, Observability of boolean control networks with time-variant delays in states, Journal of Systems Science and Complexity, 2018, 31(2): 436–445.

    Article  MathSciNet  Google Scholar 

  20. Zheng Y T, Li H T, Ding X Y, et al., Stabilization and set stabilization of delayed boolean control networks based on trajectory stabilization, Journal of the Franklin Institute-Engineering and Applied Mathematics, 2017, 354(17): 7812–7827.

    Article  MathSciNet  Google Scholar 

  21. Li Y L, Li H T, and Ding X Y, Set stability of switched delayed logical networks with application to finite-field consensus, Automatica, 2020, 113: 108768.

    Article  MathSciNet  Google Scholar 

  22. Chen H B and Zhao Y, Delay-dependent exponential stability for uncertain neutral stochastic neural networks with interval time-varying delay, International Journal of Systems Science, 2015, 46(14): 2584–2597.

    Article  MathSciNet  Google Scholar 

  23. Ding X Y, Li H T, and Wang S L, Set stability synchronization of logical networks with probabilistic time delays, Journal of the Franklin Institute-Engineering and Applied Mathematics, 2018, 355(15): 7735–7748.

    Article  MathSciNet  Google Scholar 

  24. Liu Y S, Zheng Y T, Li H T, et al., Control design for output tracking of delayed boolean control networks, Journal of Computational and Applied Mathematics, 2018, 327: 188–195.

    Article  MathSciNet  Google Scholar 

  25. Chen H W, Wu B, and Lu J Q, A minimum-time control for boolean control networks with impulsive disturbances, Applied Mathematics and Computation, 2016, 273: 477–483.

    Article  MathSciNet  Google Scholar 

  26. Xu X J, Liu Y S, Li H T, et al., Synchronization of switched boolean networks with impulsive effects, International Journal of Biomathematics, 2018, 11(6): 1850080.

    Article  MathSciNet  Google Scholar 

  27. You L J and Mu X W, Finite-time stochastic stability of random impulsive positive system, Journal of Systems Science and Complexity, 2021, 34(3): 912–923.

    Article  MathSciNet  Google Scholar 

  28. She W Q and Ma M H, Tracking synchronization of networked lagrangian systems via impulsive control and its applications, Journal of Systems Science and Complexity, 2019, 32(4): 1093–1103.

    Article  MathSciNet  Google Scholar 

  29. Li H T, Xu X J, and Ding X Y, Finite-time stability analysis of stochastic switched boolean networks with impulsive effect, Applied Mathematics and Computation, 2019, 347: 557–565.

    Article  MathSciNet  Google Scholar 

  30. Wu K N, Na M Y, Wang L M, et al., Finite-time stability of impulsive reaction-diffusion systems with and without time delay, Applied Mathematics and Computation, 2019, 363: UNSP 124591.

Download references

Author information

Authors and Affiliations

  1. School of Economics and Management, Hebei University of Technology, Tianjin, 300401, China

    Shengnan Shi

  2. School of Science, Hebei University of Technology, Tianjin, 300401, China

    Yong Xu

Authors
  1. Shengnan Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yong Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Shengnan Shi or Yong Xu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 71371186.

This paper was recommended for publication by Editor QI Hongsheng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, S., Xu, Y. Set Stability of Probabilistic Time-Delay Boolean Networks with Impulsive Effect. J Syst Sci Complex 34, 2182–2194 (2021). https://doi.org/10.1007/s11424-021-9326-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-021-9326-x

Keywords

Search

Navigation