Existence and asymptotic properties of global solution for hybrid neutral stochastic differential delay equations with colored noise

In this paper, stability of highly nonlinear hybrid neutral stochastic differential delay equations (NSDDEs) is discussed. In contrast to the white noise examined in previous literature, we incorporate colored noise into the highly nonlinear hybrid NSDDEs. Under some assumptions, we can show that highly nonlinear hybrid NSDDEs have a unique global solution. Meanwhile, we establish some criteria related to noise-to-state stability (NSS) of global solutions. Additionally, some theorems are given to guarantee asymptotic stability in $ L^{\hat{\alpha}} $ and almost surely asymptotic stability of global solution. These related discriminant rules are delay-dependent. Finally, an example is provided to demonstrate the validity of theoretical results.