Global Asymptotic Stability of a General Nonautonomous Cohen-Grossberg Model with Unbounded Amplification Functions José J. Oliveira Abstract For a class of nonautonomous differential equations with infinite delay, we give sufficient conditions for the global asymptotic stability of an equilibrium point. This class is general enough to include, as particular cases, the most of famous neural network models such as Cohen-Grossberg, Hopfield, and bidirectional associative memory. It is relevant to notice that here we obtain global stability criteria without assuming bounded amplification functions. As illustrations, results are applied to several concrete models studied in some earlier publications and new global stability criteria are given. Keywords Cohen-Grossberg neural networks · Unbounded time-varying coeffi- cients · Unbounded distributed delays · Unbounded amplification functions · Global asymptotic stability 1 Introduction The Cohen-Grossberg neural network models, first proposed and studied by Cohen and Grossberg [4] in 1983, have been the subject of an active research due to their extensive applications in various engineering and scientific areas such as neural- biology, population biology, and computing technology. The neural network model in [4] can be described by the following system of ordinary differential equations x ′ i (t ) =−a i (x i (t )) ⎡ ⎣ b i (x i (t )) − n  j=1 c ij f j (x j (t )) + I i ⎤ ⎦ , t ≥ 0, i = 1, ..., n, (1) J.J. Oliveira (B ) Centro de Matemática (CMAT), Departamento de Matemática e Aplicações, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal e-mail: jjoliveira@math.uminho.pt © Springer International Publishing Switzerland 2016 P. Gonçalves and A.J. Soares (eds.), From Particle Systems to Partial Differential Equations III, Springer Proceedings in Mathematics & Statistics 162, DOI 10.1007/978-3-319-32144-8_12 243