In this paper, conventional dynamic systems are converted to type-I and type-II linguistic dynamic systems (LDS). The evolving laws of a type-I LDS are the same as those of its conventional counterpart while Its states are linguistic. Since the evolving laws of type-I LDS are In the numerical do. main, a type-I LDS can be directly constructed from its conventional counterpart by using extension principle. The evolving laws of a type-II LDS are modeled by linguistic rules while its states are linguistic. By using extension principle, a method of converting a conventional dynamic system into a type-II LDS is presented. Based on a-cuts, the existence of fixed points of type-I LDS is studied. Also based on a-cuts, an efficient numerical procedure called acute mapping is developed for studying LDS. Numerical examples using a conventional dynamic system, namely, logistic map, are presented.