Invariant set and attractor of nonautonomous functional differential systems: a decomposition approach (Q2575240)

The paper deals with the functional-differential system \[ \dot{x}(t) = g(t,x(t)) + f(t, x(t-r(t))) + \int_{-r}^0 h(t, x(t+s))ds + p(t), \tag{1} \] where \(t \geq t_0 \geq 0, x \in \mathbb{R}^n,\) \(0 \leq r(t) \leq r\), and the continuous vector-functions \(g(t,u),f(t,u),h(t,u)\) have sublinear growth in \(u.\) Using a decomposition of matrices into nonpositive and nonnegative parts, estimations of a positive invariant set and of the global attractor of (1) are obtained. As an application, a neural network model is considered.