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This paper is concerned with relationships of Lyapunov exponents withsensitivity and stability for non-autonomous discrete systems. Some newconcepts are introduced for non-autonomous discrete systems, including Lyapunovexponents, strong sensitivity at a point and in a set, Lyapunov stability, andexponential asymptotical stability. It is shown that the positive Lyapunovexponent at a point implies strong sensitivity for a class of non-autonomousdiscrete systems. Furthermore, the uniformly positive Lyapunov exponents in atotally invariant set imply strong sensitivity in this set under certainconditions. It is also shown that the negative Lyapunov exponent at a pointimplies exponential asymptotical stability for a class of non-autonomousdiscrete systems. The related existing results for autonomous discrete systemsare generalized to non-autonomous discrete systems and their conditions areweaken. One example is provided for illustration.

Lyapunov exponents, sensitivity, and stability for non-autonomous discrete systems