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Article

Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control

by
Ning Tian
,
Xiaoqi Liu
,
Rui Kang
,
Cheng Peng
,
Jiaxi Li
and
Shang Gao
*
Department of Mathematics, Northeast Forestry University, Harbin 150040, China
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(23), 3715; https://doi.org/10.3390/math12233715
Submission received: 6 October 2024 / Revised: 14 November 2024 / Accepted: 25 November 2024 / Published: 27 November 2024
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Abstract

This paper is intended to study noise-to-state stability in probability (NSSP) for random coupled Kuramoto oscillators with input control (RCKOIC). A feedback control is designed, which makes us give the existence and uniqueness of a solution for RCKOIC. Based on Kirchhoff’s matrix tree theorem in graph theory, an original and appropriate Lyapunov function for RCKOIC is established. With the help of the Lyapunov method and by resorting to some analysis skills, NSSP for RCKOIC with an arbitrarily coupled topological structure and second-order moment process stochastic disturbance is acquired. Finally, the effectiveness of the obtained results is verified by a numerical test and its simulation process.
Keywords: noise-to-state stability; random coupled Kuramoto oscillators; feedback control; Lyapunov method; Kirchhoff’s matrix tree theorem noise-to-state stability; random coupled Kuramoto oscillators; feedback control; Lyapunov method; Kirchhoff’s matrix tree theorem

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MDPI and ACS Style

Tian, N.; Liu, X.; Kang, R.; Peng, C.; Li, J.; Gao, S. Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control. Mathematics 2024, 12, 3715. https://doi.org/10.3390/math12233715

AMA Style

Tian N, Liu X, Kang R, Peng C, Li J, Gao S. Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control. Mathematics. 2024; 12(23):3715. https://doi.org/10.3390/math12233715

Chicago/Turabian Style

Tian, Ning, Xiaoqi Liu, Rui Kang, Cheng Peng, Jiaxi Li, and Shang Gao. 2024. "Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control" Mathematics 12, no. 23: 3715. https://doi.org/10.3390/math12233715

APA Style

Tian, N., Liu, X., Kang, R., Peng, C., Li, J., & Gao, S. (2024). Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control. Mathematics, 12(23), 3715. https://doi.org/10.3390/math12233715

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