Robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay

Robust stability with general decay rate for stochastic neural networks with unbounded time-varying delays

“…To consider stability with general decay rate, let us introduce the following function ψ, which will be used as the decay function (also see [20], [22]. In [20], this decay function is named as the weight function.).…”

“…There also exists some more general stability with general decay rate (cf. [6], [16], [19], [20], [22]). These different stabilities show that speed that the solution decays to the equilibrium is different.…”

Exponential stability of numerical solution to neutral stochastic functional differential equation

“…Neutral stochastic functional differential equations have received a great deal of attention, research efforts have been devoted to stability of the analytical solutions(see [1][2][3][4][5][6]). Unfortunately, explicit solutions can rarely be obtained, especially highly nonlinear NSFDEs.…”

Exponential Stability of Neutral Stochastic Functional Differential Equations with Two-Time-Scale Markovian Switching

“…In many practical dynamical systems such as neural networks, computer aided design, population ecology, chemical process simulation, and automatic control, stochastic differential equations represent the class of important dynamics (see [1][2][3][4]). During the recent several years, the asymptotic properties of neutral stochastic functional differential equations have been investigated by many authors (see [5][6][7][8][9][10][11][12][13][14]). Mao [10,11] gave the exponential stability of neutral stochastic functional differential equations by using the Razumikhintype theorems.…”