Volume 43 Issue 2
Feb.  2022
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CAO Juan, REN Fengli. Mean-Square Synchronization and Stochastically Passive Synchronization of Delayed Gene Regulatory Networks With Markovian Switching[J]. Applied Mathematics and Mechanics, 2022, 43(2): 198-206. doi: 10.21656/1000-0887.420256
Citation: CAO Juan, REN Fengli. Mean-Square Synchronization and Stochastically Passive Synchronization of Delayed Gene Regulatory Networks With Markovian Switching[J]. Applied Mathematics and Mechanics, 2022, 43(2): 198-206. doi: 10.21656/1000-0887.420256

Mean-Square Synchronization and Stochastically Passive Synchronization of Delayed Gene Regulatory Networks With Markovian Switching

doi: 10.21656/1000-0887.420256
  • Received Date: 2021-08-31
  • Accepted Date: 2021-08-31
  • Rev Recd Date: 2021-12-15
  • Available Online: 2022-01-06
  • Publish Date: 2022-02-01
  • The research of gene regulatory networks (GRNs) and their dynamic models is important in the post-genome era. Qualitative analysis of GRNs and their dynamics is of great significance to the understanding of organisms from a systematic perspective. A stochastic GRN model with time-varying delay and Markovian switching was proposed to study the properties of mean-square synchronization and stochastically passive synchronization. Through the design of an appropriate Lyapunov-Krasovskii functional (LKF), the sufficient conditions for mean-square synchronization and stochastically passive synchronization were obtained by means of the Lyapunov stability theory, the linear matrix inequality method and the random analysis techniques. In addition, the comparison between the results of this paper and some other literatures shows that, the present results have markable theoretical meaning. The numerical simulation illustrates the validity of the obtained sufficient conditions.

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