  Periodicity plays a significant role in the chaos theory from the beginning
since the skeleton of chaos can consist of infinitely many unstable periodic
motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and
the one obtained through period-doubling cascade [3]. Countable number of
periodic orbits exist in any neighborhood of a structurally stable Poincar\'{e}
homoclinic orbit, which can be considered as a criterion for the presence of
complex dynamics [4]-[6]. It was certified by Shilnikov [7] and Seifert [8]
that it is possible to replace periodic solutions by Poisson stable or almost
periodic motions in a chaotic attractor. Despite the fact that the idea of
replacing periodic solutions by other types of regular motions is attractive,
very few results have been obtained on the subject. The present study
contributes to the chaos theory in that direction.
  In this paper, we take into account chaos both through a cascade of almost
periodic solutions and in the sense of Li-Yorke such that the original Li-Yorke
definition is modified by replacing infinitely many periodic motions with
almost periodic ones, which are separated from the motions of the scrambled
set. The theoretical results are valid for systems with arbitrary high
dimensions. Formation of the chaos is exemplified by means of unidirectionally
coupled Duffing oscillators. The controllability of the extended chaos is
demonstrated numerically by means of the Ott-Grebogi-Yorke [9] control
technique. In particular, the stabilization of tori is illustrated.
