On A nonstandard model of hybrid automaton

In this paper, we introduce an enlargement of a standard hybrid automaton (HA) called a nonstandard hybrid automaton (NHA) which is another model of HA in the domain of *ℝ rather than ℝ. We define two kinds of almost periodic trajectories called the z-*cycle and p-* cycle on NHA, and we discuss a slightly extended Zeno (*Zeno) and a limit cycle in terms of these cycles. Moreover, we classify the ω-limit set of hybrid dynamics into 4 types and present an example of NHA for each type.