Activity invariant sets and stable attractors of Lotka-Volterra recurrent neural networks

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 set can have one equilibrium point which is exponentially stable. Since the attractors are located in activity invariant sets, each attractor has binary pattern and also carries analog information. Such results can provide new perspective to apply attractor networks for applications such as group winner-take-all, associative memory, etc.