For a Young function $\phi$ and a locally compact second countable group $G,$ let $L^\phi(G)$ denote the Orlicz space on $G.$ In this paper, we present a necessary and sufficient condition for the topological transitivity of a sequence of cosine operators $\{C_n\}_{n=1}^{\infty}:=\{\frac{1}{2}(T^n_{g,w}+S^n_{g,w})\}_{n=1}^{\infty}$, defined on $L^{\phi}(G)$. We investigate the conditions for a sequence of cosine operators to be topologically mixing. Further, we go on to prove a similar result for the direct sum of a sequence of cosine operators. Finally, we give an example of topologically transitive sequence of cosine operators.
