Topic: Fast-slow decomposition

Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system 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 limits their utility especially in biological systems as their recurrent dynamics are subject to constant perturbations. We observe that the bifurcations from continuous attractors in theoretical neuroscience models display various structurall

Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for arbitrarily long time intervals. Unfortunately, because continuous attractors are not structurally stable, they suffer from severe structural instability in general---they are destroyed by most infinitesimal changes of the dynamical law that defines them. This fragility limits their utility especially in biological systems as their recurrent dynamics are subject to constant perturbations. We observe that bifurcations from and approximations of continuous attractors i

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