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Linear time series analysis, mainly the Fourier transform-based methods, has been quite successful in extracting information contained in the ever-modulating light curves of active galactic nuclei, and thereby contribute in characterizing the general features of supermassive black hole systems. In particular, the statistical properties of gamma-ray variability of blazars are found to be fairly represented by flicker noise in the temporal frequency domain. However, these conventional methods have not been able to fully encapsulate the richness and the complexity displayed in the light curves of the sources. In this work, to complement our previous study on a similar topic, we perform nonlinear time series analysis of the decade-long Fermi/LAT observations of 20 gamma-ray bright blazars. The study is motivated to address one of the most relevant queries: whether the dominant dynamical processes leading to the observed gamma-ray variability are of deterministic or stochastic nature. For the purpose, we perform recurrence quantification analysis of the blazars and directly measure the quantities, which suggest that the dynamical processes in blazars could be a combination of deterministic and stochastic processes, while some of the source light curves revealed significant deterministic content. The result, with possible implication of strong disk-jet connection in blazars, could prove to be significantly useful in constructing models that can explain the rich and complex multiwavelength observational features in active galactic nuclei. In addition, we estimate the dynamical timescales, so-called trapping timescales, in the order of a few weeks.