Stability of highly nonlinear neutral stochastic differential delay equations

Abstract

Stability criteria for neutral stochastic differential delay equations (NSDDEs) have been studied intensively for the past several decades. Most of these criteria can only be applied to NSDDEs where their coefficients are either linear or nonlinear but bounded by linear functions. This paper is concerned with the stability of hybrid NSDDEs without the linear growth condition, to which we will refer as highly nonlinear ones. The stability criteria established in this paper will be dependent on delays.

Stability of highly nonlinear hybrid stochastic integro-differential delay equations

“…Recently, [13,14] initiate the investigation on the stability of the hybrid highly nonlinear stochastic delay differential equations. Based on the highly nonlinear hybrid SDDEs (see, e.g., [13,14]), the stability of highly nonlinear systems is further explored in [6,7,8,34,35]. However, the current states of many real systems depend on several history states of some time interval.…”

Stabilisation of highly non‐linear continuous‐time hybrid stochastic differential delay equations by discrete‐time feedback control

“…Therefore, hybrid stochastic delay systems have received considerable attention (see, e.g., Mao, Matasov, and Piunovskiy (2000); Mao, and Yuan (2006); Wei, Wang, Shu, and Fang (2006); Yue, and Han (2005)). Recently, many papers have taken into account the stability of hybrid stochastic delay systems with highly nonlinear (see, e.g., Fei, Shen, Fei, Mao, and Yan (2019); Shen (2017, 2018); Hu, Mao, and Shen (2013); Shen, Fei, Mao, and Liang (2018)). In the real world, there are many hybrid stochastic systems with high nonlinearity and delay (see, e.g., Lewis (2000); Yuan, Mao, and Lygeros (2009)).…”

Analysis on structured stability of highly nonlinear pantograph stochastic differential equations

“…As we know, the hybrid systems driven by continuous-time Markov chains are often used to model systems that may experience abrupt changes in their structures and parameters caused by phenomena such as component failures or repairs (see, e.g. Mao & Yuan, 2006;Shen, Fei, Mao, & Liang, 2018;Zhou & Hu, 2016). The theory in Hu, Mao, and Zhang (2013) is good at dealing with the hybrid SDDEs that may experience abrupt changes in their parameters.…”