Discrete-Time Analogs for a Class of Continuous-Time Recurrent Neural Networks

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper is concerned with the problem of local and global asymptotic stability for a class of discrete-time recurrent neural networks, which provide discrete-time analogs to their continuous-time counterparts, i.e., continuous-time recurrent neural networks with distributed delay. Some stability criteria, which include some existing results as their special cases, are derived. A discussion about the dynamical consistence of discrete-time neural networks versus their continuous-time counterparts is provided. An <emphasis emphasistype="bold"><emphasis emphasistype="italic">unconventional finite difference method</emphasis></emphasis> is proposed and an example is also given to show the effectiveness of the method. </para>