In this paper, the dynamical properties for a sequence of cosine operators in weighted Orlicz spaces on hypergroups are investigated. Firstly, we generalize the equivalent conditions of the topological transitivity for a finite sequence of cosine operators from Orlicz spaces on locally compact group to weighted Orlicz spaces on hypergroup. Secondly, in the hypergroup setting we give some sufficient or almost necessary conditions for a sequence of cosine operators to be topologically recurrent, even topologically multiply recurrent on Orlicz spaces. Besides, we deduce that topological mixing is a sufficient or necessary condition for a sequence of cosine operators to be topologically recurrent on Orlicz spaces. Thirdly, we also obtain sufficient or necessary conditions for a sequence of cosine operators to be chaotic in Orlicz spaces on hypergroup.

This work is supported by Natural Science Foundation of Ningxia (Grant No. 2023AAC03001) and Natural Science Foundation of China(Grant Nos. 12261068, 12571088 and 12301156).