The attractor of the delayed functional-differential diffusion equation

Attracting and invariant sets for a class of impulsive functional differential equations

“…ential equations, partial differential equations and delay differential equations and so on [11][12][13][14][15][16][17][18]. Unfortunately, the corresponding problems for impulsive functional differential equations have not been considered prior to this work.…”

Attractivity of nonlinear impulsive delay differentialequations

“…Therefore, a general problem of the attractivity is to discuss the attracting set and attracting basin for the impulsive systems. Some significant progress has been made in the techniques and methods of determining the attracting set and attracting basin (domain of attraction) for the continuous systems described by ordinary differential equations [7,17] and functional differential 2 Attractivity of impulsive differential equations equations [5,9,13,15,18]. However, so far the corresponding problems for impulsive delay differential equations have not been considered.…”

Invariant and attracting sets of Hopfield neural networks with delay

“…In recent years, the invariant and attracting sets of dynamical systems have attracted considerable attention, and various interesting results on this problem have been reported (Sawano 1980, Marion 1987, GyoÈ ri 1990, Xiang 1991, Xu 1996, Hale 1997, Razgulin 1997). However, not much has been developed in the direction of the Hop® eld neural networks system.…”