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 theorem, we provide complete characterisation of the existence and uniqueness of an equilibrium of a Cohen–Grossberg–Hopfield-type neural network endowed with multiple 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.

Keywords

• cohen–grossberg–hopfield-type neural networks
• unbounded distributed time delays
• banach's contraction mapping principle
• m-matrix
• equilibrium
• lyapunov functional
• global asymptotic stability