Chronotaxic systems represent deterministic nonautonomous oscillatory systems
which are capable of resisting continuous external perturbations while having a
complex time-dependent dynamics. Until their recent introduction in \emph{Phys.
Rev. Lett.} \textbf{111}, 024101 (2013) chronotaxic systems had often been
treated as stochastic, inappropriately, and the deterministic component had
been ignored. While the previous work addressed the case of the decoupled
amplitude and phase dynamics, in this paper we develop a generalized theory of
chronotaxic systems where such decoupling is not required. The theory presented
is based on the concept of a time-dependent point attractor or a driven steady
state and on the contraction theory of dynamical systems. This simplifies the
analysis of chronotaxic systems and makes possible the identification of
chronotaxic systems with time-varying parameters. All types of chronotaxic
dynamics are classified and their properties are discussed using the
nonautonomous Poincar\'e oscillator as an example. We demonstrate that these
types differ in their transient dynamics towards a driven steady state and
according to their response to external perturbations. Various possible
realizations of chronotaxic systems are discussed, including systems with
temporal chronotaxicity and interacting chronotaxic systems.Comment: 9 pages, 8 figure
