Stability of stochastic Lévy noise coupled systems with mixed delays

Abstract

In this paper, based on Razumikhin method, stability of stochastic Lévy noise coupled systems with mixed delays (SLCSD) is researched. Here, both mixed delays and Lévy noise are considered into coupled systems for the first time. Then, by combining Razumikhin method with Lyapunov method and graph theory, several stability criteria including the Razumikhin-type theorem, the Lyapunov-type theorem and a coefficients-type theorem are given to ensure the pth moment exponential stability of SLCSD. In particular, the stability of a class of coupled oscillators and the stability of single-link robot arms are investigated as practical applications of the obtained results. And some numerical simulations are offered to illustrate the feasibility of the obtained results.

Keywords:

• Lévy noise
• Razumikhin method
• mixed delays
• coupled systems
• stability

Acknowledgements

The authors really appreciate the editor's and reviewers' valuable comments. This work was supported by the Shandong Province Natural Science Foundation (Nos. ZR2018MA005, ZR2018MA020, ZR2017MA008); the Key Project of Science and Technology of Weihai (No. 2014DXGJMS08), the Innovation Technology Funding Project in Harbin Institute of Technology (No. HIT.NSRIF.201703), the Science and Technology Program of Shenzhen, China (No. JCYJ20170818091621856) and the National Science Foundation of China (No. 61872429).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Shandong Province Natural Science Foundation [Nos. ZR2018MA005, ZR2018MA020, ZR2017MA008]; the Key Project of Science and Technology of Weihai [No. 2014DXGJMS08], the Innovation Technology Funding Project in Harbin Institute of Technology [No. HIT.NSRIF.201703], the Science and Technology Program of Shenzhen, China [No. JCYJ20170818091621856] and the National Science Foundation of China [No. 61872429].