Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks

Cheng Peng, Jiaxin Ma, Qiankun Li and Shang Gao
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Cheng Peng: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Jiaxin Ma: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Qiankun Li: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Shang Gao: Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Mathematics, 2022, vol. 10, issue 12, 1-11

Abstract: 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.

Keywords: noise-to-state stability in probability; random complex dynamical systems on network; lyapunov method; Kirchhoff’s matrix theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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