Topic: Bifurcations

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

Understanding the neural basis of animal behavior is a central challenge in biology. In this work, we establish a connection between the spatio-temporal decision-making processes of animals and the ring attractor dynamics of neurons, which determine the organism's heading direction. We formulate a neural field model within the mean field approximation to provide a microscopic description of the spontaneous formation of bifurcations along their movement trajectories towards multiple targets, as observed in recent animal experiments. The direction of movement corresponds to the position of the a

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