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

This note investigates the stabilities for impulsive stochastic delayed Cohen-Grossberg neural networks driven by Levy noise (ISDCGNNs-LN), including the input-to-state stability (ISS), integral input-to-state stability (iISS) and phi(theta)(t)-weight input-to-state stability (phi(theta)(t)-weight ISS, theta > 0). Utilizing the multiple Lyapunov-Krasovskii (L-K) functions, principle of comparison, constant variation method and average impulsive interval (AII) method, adequate ISS-type stability conditions of the ISDCGNNs-LN under stable impulse and unstable impulse are obtained. This shows that the stochastic systems are ISS in regard to a lower bound of the AII, provided that the continuous stochastic systems is ISS but has destabilizing impulse. Furthermore, the impulse can effectively stabilize the stochastic systems for a upper bound of the AII, provided that the continuous stochastic systems is not ISS. In addition, our results can also deal with the case of variable time delay. In the end, two examples are presented to reflect the rationality and correctness for the theoretical conclusions. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

This note investigates the stabilities for impulsive stochastic delayed Cohen-Grossberg neural networks driven by Levy noise. The stability conditions for input-to-state stability (ISS), integral input-to-state stability (iISS), and phi(theta)(t)-weight input-to-state stability are obtained. The results show that the stochastic systems are ISS under certain conditions, and the impulse can effectively stabilize the systems.