Abstract
The classical analysis of asymptotical and exponential stability of neural networks needs assumptions on the existence of a positive Lyapunov function $V$ and on the strict negativity of the function $dV/dt$, which often come as a result of boundedness or uniformly almost periodicity of the activation functions. In this paper, we investigate the asymptotical stability problem of Hopfield neural networks with time delays under weaker conditions. By constructing a suitable Lyapunov function, sufficient conditions are derived to guarantee global asymptotical stability and exponential stability of the equilibrium of the system. These conditions do not require the strict negativity of $dV/dt $, nor do they require that the activation functions to be bounded or uniformly almost periodic.
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