Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI
Fig 5
Example time series from an LDS-SSM and a PLRNN-SSM trained on the vdP system.
A. Example time graph (left) and state space (right) for a trajectory generated by an LDS-SSM (red) trained on the vdP system (true vdP trajectories in green). Trajectories from a LDS will almost inevitably decay toward a fixed point over time (or diverge). B. Trajectories generated by a trained PLRNN-SSM, in contrast, closely follow the vdP-system’s original limit cycle.