Devaney's Chaos for Maps on $G$-spaces

We study the notion of sensitivity on $G$-spaces and through examples observe that $G$-sensitivity neither implies nor is implied by sensitivity. Further, we obtain necessary and sufficient conditions for a map to be $G$-sensitive. Next, we define the notion of Devaney's chaos on $G$-space and show that $G$-sensitivity is a redundant condition in the definition.