The sensitivity, classical and quantum, of the cavitymediated dynamical localization to the location of the initial polariton wavepacket seen in Fig. suggest large scale changes in the classical phase space structures. As mentioned earlier, the correlation between the depopulation factor in PGH theory and enhanced phase space chaoticity has been observed earlier . Although in the present case, we are dealing with a non-dissipative system, the general idea that the emergence of regularity in the phase space with varying ω c can result in nontrivial modulations of the isomerization probability is still expected to hold true . Note that for the two dimensional model system, it is possible (see the next section) to visualize the phase space in detail using the method of Poincaré surface of sections. However, we start by computing the fast Lyapunov indicator (FLI) for the model system in order to detect the extent of chaoticity in the phase space as a function of the cavity frequency. The FLI technique is ideal for identifying chaotic, resonant, and non-resonant dynamics using short time trajectoreis . It is well known that the FLI approach has certain computational advantages and, more importantly, can be generalized to higher dimensional systems.