## 3 Results and Discussion
A noticeable change in the \(K1\) value occurs only at the highest airflow velocity, \(U\) = 10 m/s, where the indicator increases above 0.3 for almost all masses, suggesting the system transitions out of the regular motion. For the second diameter of 25 mm, when calculating \(K\) using the MSD approach, an increase in the indicator occurs at the point where the system transitions out of oscillatory behavior. This transition takes place at flow velocities between 5 and 8 m/s, inversely proportional to the average RMS results, which confirms the effectiveness of the method and its ability to capture the system's dynamics. A similar trend is observed for the largest diameter of 30 mm, where a linear increase in the \(K\)-value begins at a flow velocity of 5 m/s. When estimating the \(K2\) indicator, the transition from oscillatory dynamics to chaotic behavior is clearly visible. For the smallest diameter, 20 mm, a significant increase in the indicator occurs at a flow velocity of 10 m/s. For the remaining diameters, 25 mm and 30 mm, the behavior is similar to that observed for the indicator calculated using the MSD method; however, the \(K2\) values are noticeably higher and convey the system's dynamics more effectively. For oscillatory solutions, the \(K2\) value fluctuates around 0.2. The 0-1 test for chaos proved to be an effective tool for identifying transitions between regular and chaotic dynamics in the analyzed system. Among the two applied approaches, the covariance-based method (\(K2\)) provided higher sensitivity and clearer distinction of dynamic regimes compared to the MSD-based method (\(K1\)), especially for intermediate (25 mm) and large (30 mm) diameters. Overall, \(K2\) demonstrated better capability in  
Figure 8: Results of the 0–1 test for chaos for different bluff body diameters: (**a,b**) \(d\) = 20 mm, (**c,d**) \(d\) = 25 mm, (**e,f**) \(d\) = 30 mm. (**a,c,e**) \(K1\)—mean square displacement (MSD); (**b,d,f**) \(K2\)—Pearson correlation coefficient. capturing the onset of chaos, making it the preferred method for characterizing system behavior in this context. The observed transitions between fully oscillatory states and chaotic behavior suggest the presence of nonlinear dynamic mechanisms, which may be amplified by variations in the geometry and mass of the bluff body. Larger diameters lead to earlier flow separation, increasing the nonlinearity of the structural response. When combined with higher mass (and thus greater inertia), the system transitions more rapidly into a state of decaying vibrations, particularly in the absence of coupling with the vortex shedding frequency. The application of the 0-1 test for chaos enabled a detailed identification of transitions from regular to chaotic system behavior under varying flow conditions and geometric-mass configurations. Table 4 presents the threshold airflow velocities at which the calculated \(K\)-values exceed 0.4, indicating the onset of chaotic dynamics. Two computational approaches were used--\(K1\), based on mean square displacement (MSD), and \(K2\), based on Pearson correlation--allowing for a comprehensive assessment of the system's nonlinear response. The results show that the correlation-based method (\(K2\)) consistently provides clearer and more sensitive detection of transitions across all tested cases, particularly for bluff bodies with intermediate (25 mm) and large (30 mm) diameters. These configurations exhibited earlier transitions into chaos, confirming the significant role of aerodynamic blockage and inertial effects. In contrast, for the smallest diameter (20 mm), chaotic behavior was observed only at the highest flow velocities, and, in several cases, no transition was detected, indicating sustained regular oscillations. These findings underline the effectiveness of the 0-1 test, especially the covariance-based variant, in detecting complex dynamic changes and reinforce the influence of both geometric and mass parameters on the stability and chaoticity of the system.