1 research outputs found
Lyapunov exponents, sensitivity, and stability for non-autonomous discrete systems
This paper is concerned with relationships of Lyapunov exponents with
sensitivity and stability for non-autonomous discrete systems. Some new
concepts are introduced for non-autonomous discrete systems, including Lyapunov
exponents, strong sensitivity at a point and in a set, Lyapunov stability, and
exponential asymptotical stability. It is shown that the positive Lyapunov
exponent at a point implies strong sensitivity for a class of non-autonomous
discrete systems. Furthermore, the uniformly positive Lyapunov exponents in a
totally invariant set imply strong sensitivity in this set under certain
conditions. It is also shown that the negative Lyapunov exponent at a point
implies exponential asymptotical stability for a class of non-autonomous
discrete systems. The related existing results for autonomous discrete systems
are generalized to non-autonomous discrete systems and their conditions are
weaken. One example is provided for illustration.Comment: 11 page