Continuous attractors of recurrent neural networks with complex-valued weights

The global exponential stability (GAS), global asymptotic stability (GES) and multi-stability (MS) continuous attractors of recurrent neural networks (RNN) with complex-valued weights are studied in this paper. As a continuous attractor is the infinite equilibria, the connected matrix needs to be nonsingular. Therefore, RNN is transformed into a lower dimensional RNN using elementary operation. Firstly, based on the foregoing results some continuous attractors of RNN with real-valued weights are obtained. Secondly, continuous attractors of RNN with complex-valued weights are obtained by studying the corresponding RNN with real-valued weights. Some simulations are finally carried out to illustrate the theory.