  The Higgs amplitude mode of the order parameter of an ultracold confined
Fermi gas in the BCS regime after a quench of the coupling constant is analyzed
theoretically. Characteristic features are a damped oscillation which at a
certain transition time changes into a rather irregular dynamics. We compare
the numerical solution of the full set of nonlinear equations of motion for the
normal and anomalous Bogoliubov quasiparticle excitations with a linearized
approximation. In doing so the transition time as well as the difference
between resonant systems, i.e., systems where the Fermi energy is close to a
subband minimum, and off-resonant systems can be well understood and traced
back to the system and geometry parameters.
