Continuous Recurrent Neural Networks Based on Function Satlins Coexistence of Multiple Continuous Attractors

The brief investigates the coexistence of multiple continuous attractors in a recurrent neural network, i.e., the symmetric saturated Satlins linear neural networks, based on a parameterized 2-D model. The saturated parts of the unliner activation function are the breakthrough for us to study the coexistence. The novel point of our research method is linearization in nonlinear networks. A continuous attractor is a set of connected stable equilibrium points. On the basis of the theorem that we proved on stability and existing findings on equilibria in mathematics, we propose the conditions for the coexistence of two or even multiple continuous attractors in a recurrent neural network. Simulations are also demonstrated to illustrate the theoretical results.