Existence, uniqueness, and global asymptotic stability of an equilibrium in a multiple unbounded distributed delay network

Abstract

By employing the notion of M-matrices and Banach’s contraction mapping principle, we provide complete characterisation of the existence and uniqueness of an equilibrium of a Cohen–Grossberg–Hopfield-type neural network endowed with multiple unbounded distributed time delays. Invoking similar arguments, and by constructing a suitable Lyapunov functional, we establish sufficient conditions for the global asymptotic stability of the equilibrium, independent of time delays.