This study examined the recurrence patterns of Earth's polar cap activities in response to various geomagnetic storm intensities. Time series data of polar cap indices (PCN and PCS) for great storm, severe storm, strong storm, moderate storm, and weak storm events were analysed. Nonlinear dynamics tools, including Recurrence Plot (RP), Recurrence Rate (RR), and Length of Diagonal Line (L), were applied to the polar cap variations to identify the recurring patterns associated with the various categories of geomagnetic storms. The RP, RR, and L effectively captured the distinct recurrence features in the PCN and PCS variations across different storm categories. During great storms, severe storms, and strong geomagnetic storms, the RPs unveils a strong deterministic structure for both PCN and PCS variations, whereas moderate and weak storms showed a rare deterministic structure of RP. Similarly, RR and L values were high during great storms, severe storms, and strong storms, however these indicators significantly decline during moderate and weak storms. These findings indicates that the recurrence density and deterministic behaviour in the polar cap activities, intensify with increased solar wind energy input into the magnetosphere.