Razumikhin-type theorems on general decay stability of stochastic functional differential equations with infinite delay

A new method for exponential stability of coupled reaction–diffusion systems with mixed delays: Combining Razumikhin method with graph theory

“…Recently, the stability of many kinds of systems is studied by Lyapunov method [10,[38][39][40][41]. In addition, Razumikhin method is also used to investigate various kinds of stability of systems [20][21][22][23][24][25][26]. Theorem 1 presents a sufficient criterion to guarantee the exponential stability of CRDSMD (1), and it is called the Razumikhin-type theorem.…”

“…Compared with the Lyapunov functional method, the imposed conditions of Razumikhin method have fewer restrictions. Recently, the Razumikhin-type stability theorem for different kinds of dynamical systems was established in [20][21][22][23][24][25][26]. It is obvious to see that the Razumikhin method provides a powerful way to study the stability of delayed differential equations from the previous literatures.…”

P-th moment and almost sure stability of stochastic switched nonlinear systems

“…(2008), Wu and Hu (2012) and Pavlovic and Jankovic (2012), the researchers introduce -type function and investigate p-th moment and almost surely stability for stochastic nonlinear systems. Since stability contains exponential stability and polynomial stability, it has a wide applicability.…”

Razumikhin-Type Theorems on General Decay Stability of Impulsive Stochastic Functional Differential Systems with Markovian Switching

“…Later, this technique was appropriately developed and extended to some other stochastic functional differential systems, especially important in applications, such as stochastic functional differential systems with infinite delay [14]- [16], hybrid stochastic delay interval systems [17] and impulsive stochastic delay differential systems [18]- [20]. Recently, some researchers have introduced ψ-type function and extended the stability results to the general decay stability, including the exponential stability as a special case in [21]- [23], which has a wide applicability.…”