Abstract
Extracting dynamics from point processes produced by different models describing spiking phenomena depends on several factors affecting the quality of reconstruction of nonuniformly sampled dynamical systems. Although its ability is verified by embedding theorems analogous to the Takens theorem for uniformly sampled time series, a limited amount of samples, a low firing rate and the presence of noise can provide significant computational errors and incorrect characterization of the analyzed oscillatory regimes. Here, we discuss how to improve the accuracy of the quantitative evaluation of complex oscillations from point processes using data resampling. This approach provides a more stable estimation of Lyapunov exponents for noisy datasets. The advantages of resampling-based reconstruction are confirmed by the analysis of various spiking mechanisms, including the generation of single firing events and chaotic bursts.
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