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Since the COVID-19 pandemic was first reported in 2019, it has rapidly spread around the world. Many countries implemented several measures to try to control the virus spreading. The healthcare system and consequently the general quality of life population in the cities have all been significantly impacted by the Coronavirus pandemic. The different waves of contagious were responsible for the increase in the number of cases that, unfortunately, many times lead to death. In this paper, we aim to characterize the dynamics of the six waves of cases and deaths caused by COVID-19 in Rio de Janeiro city using techniques such as the Poincare plot, approximate entropy, second-order difference plot, and central tendency measures. Our results reveal that by examining the structure and patterns of the time series, using a set of non-linear techniques we can gain a better understanding of the role of multiple waves of COVID-19, also, we can identify underlying dynamics of disease spreading and extract meaningful information about the dynamical behavior of epidemiological time series. Such findings can help to closely approximate the dynamics of virus spread and obtain a correlation between the different stages of the disease, allowing us to identify and categorize the stages due to different virus variants that are reflected in the time series. [ABSTRACT FROM AUTHOR]