Characterizing chaotic dynamics from integrate-and-fire (IF) interspike intervals (ISIs) is relatively easy performed at high firing rates. When the firing rate is low, a correct estimation of Lyapunov exponents (LEs) describing dynamical features of complex oscillations reflected in the IF ISI sequences becomes more complicated. In this work we discuss peculiarities and limitations of quantifying chaotic dynamics from IF point processes. We consider main factors leading to underestimated LEs and demonstrate a way of improving numerical determining of LEs from IF ISI sequences. We show that estimations of the two largest LEs can be performed using around 400 mean periods of chaotic oscillations in the regime of phase-coherent chaos. Application to real data is discussed.
Radioactivity was measured for 170 cow's milk samples in Salah-Din governorate. Samples were measured by a gamma spectrometry system, using a high purity germanium (HPGe) detector. The detector was shielded by 10 cm all sides with cadmium copper in the inner sides. The selected characteristic gamma peaks for the detection of different ware 1460kev for K-40. The energy calibration was performed using a set of standard gamma ray calibration sources Eu-152. The results of show the presence of in all samples of milk. The maximum radioactivity was seen in Baiji city was (424 Bq/kg), while the minimum was seen in Abayaji (256 Bq/kg) and the average of all samples was (341.3 Bq/kg) and the annual effective dose was 0.302`mSv/y.That considered as the annual limit of rang of public recommended by the FAO.
We discuss the problem of the detection of hyperchaotic oscillations in coupled nonlinear systems when the available information about this complex dynamical regime is very limited. We demonstrate the ability of diagnosing the chaos-hyperchaos transition from return times into a Poincaré section and show that an appropriate selection of the secant plane allows a correct estimation of two positive Lyapunov exponents (LEs) from even a single sequence of return times. We propose a generalized approach for extracting dynamics from point processes that allows avoiding spurious identification of the dynamical regime caused by artifacts. The estimated LEs are nearly close to their expected values if the second positive LE is essentially different from the largest one. If both exponents become nearly close, an underestimation of the second LE may be obtained. Nevertheless, distinctions between chaotic and hyperchaotic regimes are clearly possible.
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