Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1545-1554.

### The Collectively Sensitivity and Accessible in Non-Autonomous Composite Systems

Xiaofang Yang1(),Xiao Tang2(),Tianxiu Lu1,3,*()

1. 1 College of Mathematics and Statistics, Sichuan University of Science and Engineering, Sichuan Zigong 643000
2 School of Mathematical Science, Sichuan Normal University, Chengdu 610068
3 Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Sichuan Zigong 643000
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.