  An autoresonant approach for exciting space-time quasicrystals in
Bose-Einstein condensates is proposed by employing two-component chirped
frequency parametric driving or modulation of the interaction strength within
Gross-Pitaevskii equation. A weakly nonlinear theory of the process is
developed using Whitham's averaged variational principle yielding reduction to
a two-degrees-of-freedom dynamical system in action-angle variables.
Additionally, the theory also delineates permissible driving parameters and
establishes thresholds on the driving amplitudes required for autoresonant
excitation.
