| In this paper, a new types of stability were extend for two different systems, Differential system and Difference system; There are two chapter in this paper, in the first chapter we extended these new types of stability, namely relative (stability to two functional differential systems and gave some results of relative instability using cone and cone-valued Lyapunov functional. In the second chapter we investigated the new types of stability, namely instability of comparison difference equations, at the same time, various stability results for a very general system of difference equations were obtained via the method of cone-valued functions and comparison principle.
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