Automatical Knowledge Representation of Logical Relations by Dynamical Neural Network

Currently, most artificial neural networks (ANNs) represent relations, such as back-propagation neural network, in the manner of functional approximation. This kind of ANN is good at representing the numeric relations or ratios between things. However, for representing logical relations, these ANNs have disadvantages because their representation is in the form of ratio. Therefore, to represent logical relations directly, we propose a novel ANN model called probabilistic logical dynamical neural network (PLDNN). Inhibitory links are introduced to connect exciting links rather than neurons so as to inhibit the connected exciting links conditionally to make them represent logical relations correctly. The probabilities are assigned to the weights of links to indicate the belief degree in logical relations under uncertain situations. Moreover, the network structure of PLDNN is less limited in topology than traditional ANNs, and it is dynamically built completely according to the data to make it adaptive. PLDNN uses both the weights of links and the interconnection structure to memorize more information. The model could be applied to represent logical relations as the complement to numeric ANNs.

Input-to-State Stability for Dynamical Neural Networks with Time-Varying Delays

A class of dynamical neural network models with time-varying delays is considered. By employing the Lyapunov-Krasovskii functional method and linear matrix inequalities (LMIs) technique, some new sufficient conditions ensuring the input-to-state stability (ISS) property of the nonlinear network systems are obtained. Finally, numerical examples are provided to illustrate the efficiency of the derived results.