Even type Lyapunov functions were constructed based on M-matrix theory to study the globally
asymptotic stability of Hopfield networks with reaction-diffusion. These networks are generalized without
assuming the boundedness, monotonicity and differenciability of the activate functions. The conditions were
obtained for globally asymptotic stability of the generalized Hopfield networks, where the interconnection
matrices are symmetric or non-asymmetric and the neural activate functions are non-monotonic.