We investigate localized neutron flux perturbations in the CROCUS zero-power reactor, using both experiments and simulation. Reactivity is varied by means of a dedicated oscillation system that precisely inserts cylindrical samples of absorbing materials, namely tantalum (Ta), tungsten (W), and gold (Au), into a core channel. The resulting flux response is recorded by the high-resolution SAFFRON detection array, which provides insights both on the localized evolution within millimeters of the perturbation point. These measurements are then used to validate two features of the Monte Carlo code TRIPOLI-4®: the kinetic simulation mode, which is capable of solving the time-dependent Boltzmann equation coupled to the delayed neutron precursor equations, and the asymptotic reactor period calculations.