Abstract:

In this paper, collectively sensitivity, collectively infinity sensitivity, collectively Li-Yorke sensitivity and collectively accessible are defined in the non-autonomous discrete system. First of all, it is showed that, on compact metric spaces, mapping sequence $(f_k)^\infty_{k=1}$ is ${\cal P}$-chaos if and only if $ \forall n\in {\Bbb N}$ ($N$ is the set of natural numbers and does not contain 0). Then, under the condition that $f_{1, \infty}$ is uniformly convergence, it is proved that $f_{1, \infty}$ is ${\cal CP}$-chaos if and only if for any $m\in {\Bbb N}$, $f_{1, \infty}^{[m]}$ is ${\cal CP}$-chaos. Where ${\cal P}$-chaos denote one of the five properties: transitivity, sensitivity, infinitely sensitivity, accessibility and exact, ${\cal CP}$-chaos denote one of the four properties: collectively sensitivity, collectively infinity sensitivity, collectively Li-Yorke sensitivity and collectively accessible.

Key words: Non-autonomous discrete system, Composite mapping, Transitivity, Sensitivity, Accessibility