@article{Shen2026, 
author = {Mingxuan Shen and Huayu Wang and Chunhui Mei},
title = {Delay-dependent stability of highly nonlinear neutral stochastic systems with non-differentiable delay},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {3},
pages = {1988-2008},
keywords = {neutral stochastic differential equations, M-matrix, delay-dependent stability, non-differentiable delay, Lyapunov functional},
url = {https://www.sciopen.com/article/10.3934/era.2026089},
doi = {10.3934/era.2026089},
abstract = {The aim of this paper is to investigate the delay-dependent stability of highly nonlinear hybrid neutral stochastic differential delay equations (NSDDEs). Departing from most existing studies, the system under consideration incorporates a time-varying delay that is not required to be differentiable. A novel decomposition scheme for the drift coefficient is introduced, relaxing the conventional restrictive Lipschitz condition on the delay component. By constructing appropriate Lyapunov functionals and employing an M-matrix approach, delay-dependent conditions are derived to ensure moment stability for the considered highly nonlinear NSDDEs. Finally, an example is given to demonstrate the effectiveness of our new theory.}
}