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The concepts of selectable and unselectable sets are proposed to describe some interesting dynamical properties of a class of recurrent neural networks (RNNs) with saturated piecewise linear transfer function. A set of neurons is said to be selectable if it can be co-unsaturated at a stable equilibrium point by some external input. A set of neurons is said to be unselectable if it is not selectable,...
This paper proposes to study the activity invariant sets and exponentially stable attractors of Lotka-Volterra recurrent neural networks. The concept of activity invariant sets deeply describes the property of an invariant set by that the activity of some neurons keeps invariant all the time. Conditions are obtained for locating activity invariant sets. Under some conditions, it shows that an invariant...
The convergence of background neural networks with two identical, unstructured subnetworks that inhibit each other is studied. The convergence properties include global attractivity and complete stability analysis. Furthermore, it shows that shifting the background level affects the existence and stability of the equilibrium point. Adding noise to the networks, it will fluctuate around an equilibrium...
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