Exponential stability of stochastic complex networks with multi-weights driven by second-order process based on graph theory

Fan Yang; Xiaohui Ai; Fan Yang; Xiaohui Ai

doi:10.3934/math.2024482

AIMS Mathematics

2024, Volume 9, Issue 4: 9847-9866. doi: 10.3934/math.2024482

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Research article

Exponential stability of stochastic complex networks with multi-weights driven by second-order process based on graph theory

Fan Yang ,
Xiaohui Ai ^,

Department of Mathematics, Northeast Forestry University, Harbin, China

Received: 01 January 2024 Revised: 22 February 2024 Accepted: 29 February 2024 Published: 12 March 2024
MSC : 05C82, 39A50, 60G12, 93D23

Stochastic complex networks with multi-weights which were driven by Brownian motion were widely investigated by many researchers. However, Brownian motion is not suitable for the modeling of engineering issues by reason of its variance, which is infinite at any time. So, in this paper, a novel kind of stochastic complex network with multi-weights driven by second-order process is developed. To disclose how the weights and second-order process affect the dynamical properties of stochastic complex networks with multi-weights driven by the second-order process, we discuss exponential stability of the system. Two types of sufficient criteria are provided to ascertain exponential stability of the system on the basis of Kirchhoff's matrix tree theorem and the Lyapunov method. Finally, some numerical examples are given to verify the correctness and validity of our results.
- stochastic complex networks,
- multi-weights,
- exponential stability,
- second-order process,
- graph theory
Citation: Fan Yang, Xiaohui Ai. Exponential stability of stochastic complex networks with multi-weights driven by second-order process based on graph theory[J]. AIMS Mathematics, 2024, 9(4): 9847-9866. doi: 10.3934/math.2024482

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Abstract

Stochastic complex networks with multi-weights which were driven by Brownian motion were widely investigated by many researchers. However, Brownian motion is not suitable for the modeling of engineering issues by reason of its variance, which is infinite at any time. So, in this paper, a novel kind of stochastic complex network with multi-weights driven by second-order process is developed. To disclose how the weights and second-order process affect the dynamical properties of stochastic complex networks with multi-weights driven by the second-order process, we discuss exponential stability of the system. Two types of sufficient criteria are provided to ascertain exponential stability of the system on the basis of Kirchhoff's matrix tree theorem and the Lyapunov method. Finally, some numerical examples are given to verify the correctness and validity of our results.

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