  In this paper we study the dynamics of a general non-autonomous dynamical
system generated by a family of continuous self maps on a compact space $X$. We
derive necessary and sufficient conditions for the system to exhibit complex
dynamical behavior. In the process we discuss properties like transitivity,
weakly mixing, topologically mixing, minimality, sensitivity, topological
entropy and Li-Yorke chaoticity for the non-autonomous system. We also give
examples to prove that the dynamical behavior of the non-autonomous system in
general cannot be characterized in terms of the dynamical behavior of its
generating functions.
