Abstract
In this paper, we consider the asymptotic stability for the system of linear delay differential equations. Because of the complicated interactions induced by the delay effects of the system, there are few results of the asymptotic stability for the system of the delay differential equations with multiple delays. Given this fact, we propose the new stability conditions for the system and apply these conditions to some mathematical models for the population dynamics and neural network system described by the system of delay differential equations.
Acknowledgments
The authors would like to express their sincere gratitude to Professor Hideo Kubo for his feedback and valuable advices.
The work of the first author is partially supported by MEXT through Program for Leading Graduate Schools (Hokkaido University “Ambitious Leader's Program").
The work of the fourth author is partially supported by Grant-in-Aid for Scientific Research (C) No. 18K03369 from Japan Society for the Promotion of Science.
The authors also would like to thank the anonymous referee for helpful and valuable comments on the paper.
Citation
Ikki Fukuda. Yuya Kiri. Wataru Saito. Yoshihiro Ueda. "Stability Criteria for the System of Delay Differential Equations and its Applications." Osaka J. Math. 59 (1) 235 - 251, January 2022.
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