  We develop an explicit description of a time-dependent response of fermionic
condensates to perturbations. The dynamics of Cooper pairs at times shorter
than the energy relaxation time can be described by the BCS model. We obtain a
general explicit solution for the dynamics of the BCS model. We also solve a
closely related dynamical problem - the central spin model, which describes a
localized spin coupled to a "spin bath". Here, we focus on presenting the
solution and describing its general properties, but also mention some
applications, e.g. to nonstationary pairing in cold Fermi gases and to the
issue of electron spin decoherence in quantum dots. A typical dynamics of the
BCS and central spin models is quasi-periodic with a large number of
frequencies and stable under small perturbations. We show that for certain
special initial conditions the number of frequencies decreases and the solution
simplifies. In particular, periodic solutions correspond to the ground state
and excitations of the BCS model.
