Robustness of hybrid neutral differential systems perturbed by noise

Abstract

This paper considers a given neutral functional system under regime switching whose solution grows at most polynomially. Can the system tolerate Brownian noise and colour noise to preserve the polynomial growth if the system is subject to another environment noise? The answer is positive. This paper shows that environmental noise and regime switching work together to make the original neutral differential system whose solution grows at most polynomially become a new neutral functional differential system whose solution will still preserve polynomial growth. This indicates that this neutral functional differential system can tolerate small noise without losing the property of polynomial growth, which implies robustness. This paper also proves that the criterion is suitable to neutral delay system which is as a special case of functional system. Finally, two examples are given to illustrate the main theory.