  We investigate the life cycle of the large amplitude Higgs mode in strongly
interacting superfluid Fermi gas. Through numerical simulations with
time-dependent density-functional theory and the technique of the interaction
quench, we verify the previous theoretical predictions on the mode's frequency.
Next, we demonstrate that the mode is dynamically unstable against external
perturbation and qualitatively examine the emerging state after the mode
decays. The post-decay state is characterized by spatial fluctuations of the
order parameter and density at scales comparable to the superfluid coherence
length scale. We identify similarities with FFLO states, which become more
prominent at higher dimensionalities and nonzero spin imbalances.
