In this paper, we analyze the dynamic effect of a reservoir computer (RC) on its performance. Modified Kuramoto's coupled oscillators are used to model the RC, and synchronization, Lyapunov spectrum (and dimension), Shannon entropy, and the upper bound of the Kolmogorov-Sinai entropy are employed to characterize the dynamics of the RC. The performance of the RC is analyzed by reproducing the distribution of random, Gaussian, and quantum jumps series (shelved states) since a replica of the time evolution of a completely random series is not possible to generate. We demonstrate that hyperchaotic motion, moderate Shannon entropy, and a higher degree of synchronization of Kuramoto's oscillators lead to the best performance of the RC. Therefore, an appropriate balance of irregularity and order in the oscillator's dynamics leads to better performances., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)