Instability of stochastic differential systems with impulsive effects

Abstract

This paper considers the problem of the instability issues of stochastic differential systems with impulsive effects. Definitions of instability including almost sure exponential instability, pth moment exponential instability and pth moment instability are given. By using the Lyapunov functions, the comparison theorem and the average impulsive interval condition, several instability criteria are established. Three examples are given to illustrate the effectiveness of the theoretical results.

Keywords:

• Stochastic systems
• impulsive effects
• instability
• Lyapunov function

Disclosure statement

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

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (11771001), the Key Natural Science Research Project of Universities of Anhui Province, China (2022AH050108, 22020721025, KJ2019A0047, KJ2020A0121), the Natural Science Foundation of Anhui Province (K120131028).