In this thesis, we introduce different versions of Barbalat’s lemma, including Barbalat’s lemma in discrete system,continuous system and stochastic system. From now on, we call Barbalat’s lemma as deterministic Barbalat’s lemma, in order to distinguish with stochastic Barbalat’s lemma. Then, we discuss applications in different and important collective dynamics models.In fact, we also have some similar theorems or principles which can give us similar conclusions. What is more, sometimes we can only use one of these theorems in some specific cases. Therefore, we compare the differences and similarities between these theoremsand discuss which kind of theorem can be used for various kinds of problems.