Stability analysis of impulsive stochastic delayed Cohen-Grossberg neural networks driven by Lévy noise

Highlights：

• Comparison principle, Lyapunov-Krasovskii function, average impulsive interval and constant variation method are utilized for two situations: continuous ISS system under destabilizing impulse and continuous non-ISS systems under stabilizing impulse.

• The ISS with a general decay rate (i.e. the θ in this paper) is more general than the ISS of exponential type.

• Our theoretical results can deal with the case of variable time delay.

• We consider the impulsive delayed Cohen-Grossberg neural networks driven by Lévy noise, which is an extension of some models which have been studied more in recent years.

摘要

•The input-to-state stability (ISS), integral input-to-state stability (iISS) and ϕθ(t)-weight input-to-state stability (ϕθ(t)-weight ISS, θ>0) of the time delayed impulsive neural networks are studied comprehensively and the utilized ϕ-type function makes the stability consequence more general and less conservative.•Comparison principle, Lyapunov-Krasovskii function, average impulsive interval and constant variation method are utilized for two situations: continuous ISS system under destabilizing impulse and continuous non-ISS systems under stabilizing impulse.•The ISS with a general decay rate (i.e. the θ in this paper) is more general than the ISS of exponential type.•Our theoretical results can deal with the case of variable time delay.•We consider the impulsive delayed Cohen-Grossberg neural networks driven by Lévy noise, which is an extension of some models which have been studied more in recent years.