Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI
Fig 9
Examples of highly nonlinear phenomena extracted from fMRI data (in systems with M = 10 states, no external inputs).
A. PLRNN-BOLD-SSM with 3 stable limit cycles (LC) estimated from one subject (top: subspace of state space for 3 selected states; bottom: time graphs). B. PLRNN with 2 stable limit cycles and one chaotic attractor, estimated from another subject. C. PLRNN with one stable limit cycle and one stable fixed point. D. Increase in average (log Euclidean) distance between initially infinitesimally close trajectories with time for chaotic attractor in B. (In A and B states diverging towards–∞ were removed, as by virtue of the ReLU transformation they would not affect the other states and hence overall dynamics).