Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks
This paper studies noise-to-state stability in probability (NSSP) for random complex dynamical systems on networks (RCDSN). On the basis of Kirchhoff’s matrix theorem in graph theory, an appropriate Lyapunov function which combines with every subsystem for RCDSN is established. Moreover, some suffic...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/12/2096 |
| _version_ | 1797484665744916480 |
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| author | Cheng Peng Jiaxin Ma Qiankun Li Shang Gao |
| author_facet | Cheng Peng Jiaxin Ma Qiankun Li Shang Gao |
| author_sort | Cheng Peng |
| collection | DOAJ |
| description | This paper studies noise-to-state stability in probability (NSSP) for random complex dynamical systems on networks (RCDSN). On the basis of Kirchhoff’s matrix theorem in graph theory, an appropriate Lyapunov function which combines with every subsystem for RCDSN is established. Moreover, some sufficient criteria closely related to the topological structure of RCDSN are given to guarantee RCDSN to meet NSSP by means of the Lyapunov method and stochastic analysis techniques. Finally, to show the usefulness and feasibility of theoretical findings, we apply them to random coupled oscillators on networks (RCON), and some numerical tests are given. |
| first_indexed | 2024-03-09T23:07:39Z |
| format | Article |
| id | doaj.art-37d3af63af4441c09a6ed74839c457d6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:07:39Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-37d3af63af4441c09a6ed74839c457d62023-11-23T17:49:38ZengMDPI AGMathematics2227-73902022-06-011012209610.3390/math10122096Noise-to-State Stability in Probability for Random Complex Dynamical Systems on NetworksCheng Peng0Jiaxin Ma1Qiankun Li2Shang Gao3Department of Mathematics, Northeast Forestry University, Harbin 150040, ChinaDepartment of Mathematics, Northeast Forestry University, Harbin 150040, ChinaDepartment of Mathematics, Northeast Forestry University, Harbin 150040, ChinaDepartment of Mathematics, Northeast Forestry University, Harbin 150040, ChinaThis paper studies noise-to-state stability in probability (NSSP) for random complex dynamical systems on networks (RCDSN). On the basis of Kirchhoff’s matrix theorem in graph theory, an appropriate Lyapunov function which combines with every subsystem for RCDSN is established. Moreover, some sufficient criteria closely related to the topological structure of RCDSN are given to guarantee RCDSN to meet NSSP by means of the Lyapunov method and stochastic analysis techniques. Finally, to show the usefulness and feasibility of theoretical findings, we apply them to random coupled oscillators on networks (RCON), and some numerical tests are given.https://www.mdpi.com/2227-7390/10/12/2096noise-to-state stability in probabilityrandom complex dynamical systems on networklyapunov methodKirchhoff’s matrix theorem |
| spellingShingle | Cheng Peng Jiaxin Ma Qiankun Li Shang Gao Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks Mathematics noise-to-state stability in probability random complex dynamical systems on network lyapunov method Kirchhoff’s matrix theorem |
| title | Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks |
| title_full | Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks |
| title_fullStr | Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks |
| title_full_unstemmed | Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks |
| title_short | Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks |
| title_sort | noise to state stability in probability for random complex dynamical systems on networks |
| topic | noise-to-state stability in probability random complex dynamical systems on network lyapunov method Kirchhoff’s matrix theorem |
| url | https://www.mdpi.com/2227-7390/10/12/2096 |
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