Practical Exponential Stability of Impulsive Stochastic Food Chain System with Time-Varying Delays

This paper studies the practical exponential stability of an impulsive stochastic food chain system with time-varying delays (ISOFCSs). By constructing an auxiliary system equivalent to the original system and comparison theorem, the existence of global positive solutions to the suggested system is discussed. Moreover, we investigate the sufficient conditions for the exponential stability and practical exponential stability of the system, which is given by Razumikhin technique and the Lyapunov method. In addition, when Razumikhin's condition holds, the exponential stability and practical exponential stability of species are independent of time delay. Finally, numerical simulation finds the validity of the method.

Automated summary

This paper examines the practical exponential stability of an impulsive stochastic food chain system with time-varying delays. The existence of global positive solutions to the suggested system is discussed by constructing an auxiliary system equivalent to the original system and comparison theorem. Furthermore, the sufficient conditions for the exponential stability and practical exponential stability of the system are investigated using Razumikhin technique and the Lyapunov method. Additionally, the exponential stability and practical exponential stability of species are independent of time delay when Razumikhin's condition holds. The validity of the method is confirmed through numerical simulation.