This paper primarily investigates the (r, s)-sensitivity and its stronger variants in dynamical systems. We first prove that chain mixing systems with the shadowing property exhibit strong multi- \(\beta\) -n-sensitivity and strong \(\beta\) -n-sensitivity under the condition of surjection. We improve Theorem 5(i) in T.K.S. Moothathu. J Differ Equ Appl. (18), establishing the equivalence between: (i) (X, T) is sensitive. (ii) (X, T) has \(\mathcal {P}\) -(r, s)-sensitive pairs almost everywhere for every \(r,s\in \mathbb {N}\) . (iii) (X, T) is \(\mathcal {P}\) -(r, s)-sensitive for every \(r,s\in \mathbb {N}\) . Furthermore, we demonstrate that multi-transitivity is strictly stronger than \(\beta\) -n-sensitivity for any, and investigate how multi-(r, s)-sensitivity and (r, s)-sensitivity are transmitted to the hyperspace and product dynamical systems. Finally, we define strong \(\beta\) -shadowing property and prove that it is equivalent to the classical shadowing property.
