Topic: recurrent neural states

Continuous attractors offer a unique class of dynamical systems solutions for storing continuous-valued variables in recurrent neural states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability in general---they are destroyed by most infinitesimal changes of the dynamical law that defines them. This fragility may limit their utility especially in biological systems as their recurrent dynamics are subject to constant perturbations. We indeed observe that the bifurcations from continuous attractors in theoretical neuroscience models