The photoplethysmogram is widely used in medical settings and sports equipment to measure biological signals. The photoplethysmogram, which is measured noninvasively, can provide valuable information about cardiovascular system performance. The present study sought to investigate the underlying dynamics of photoplethysmographic signals from healthy young human subjects. In previous studies the photoplethysmogram was claimed to be driven by deterministic chaos [Tsuda 1992, Sumida 2000]; however, the methods applied for chaos detection were noise sensitive and inconclusive. Therefore, to reach a consistent conclusion it is important to employ additional nonlinear time series analysis tools that can test different features of the signal's underlying dynamics. In this paper, methods of nonlinear time series analysis, including time delay embedding, largest Lyapunov exponent, deterministic nonlinear prediction, Poincaré section, the Wayland test and method of surrogate data were applied to photoplethysmogram time series to identify the unique characteristics of the photoplethysmogram as a dynamical system. Results demonstrated that photoplethysmogram dynamics is consistent with the definition of chaotic movement, and its chaotic properties showed some similarity to Rossler's single band chaos with induced dynamical noise. Additionally it was found that deterministic nonlinear prediction, Poincaré section and the Wayland test can reveal important characteristics of photoplethysmographic signals that will be important tools for theoretical and applied studies on the photoplethysmogram

Noise contamination in experimental data with underlying chaotic dynamics is one of the significant problems limiting the application of many nonlinear time series analysis methods. Although numerous studies have been devoted to the investigation of different aspects of noise—nonlinear dynamics interactions, the effects produced by noise on chaotic dynamics are not fully understood. This study sought to analyze the local effects produced by noise on chaotic dynamics with a smooth attractor. Local Wayland test translation errors were calculated for noise-induced Lorenz and Rössler chaotic models, and for experimental green light photoplethysmogram data. Results demonstrated that under noise induction, local regions on the chaotic attractor with high values of local translation error can be observed. This phenomenon was defined as the local noise sensitivity. It was found that for both models, local noise-sensitive regions were located close to the system's equilibrium points. Additionally, it was found that the reconstructed dynamics represent well the local noise sensitivity of the original dynamics. The concept of local noise sensitivity is expected to contribute to various applied studies, as it reveals regions of chaotic attractors that are sensitive to the presence of noise.

Real-world processes are often combinations of deterministic and stochastic processes. Soil failure observed during farm tillage is one example of this phenomenon. In this paper, we investigated the nonlinear features of soil failure patterns in a farm tillage process. We demonstrate emerging determinism in soil failure patterns from stochastic processes under specific soil conditions. We normalized the deterministic nonlinear prediction considering autocorrelation and propose it as a robust way of extracting a nonlinear dynamical system from noise contaminated motion. Soil is a typical granular material. The results obtained here are expected to be applicable to granular materials in general. From a global scale to nano scale, the granular material is featured in seismology, geotechnology, soil mechanics, and particle technology. The results and discussions presented here are applicable in these wide research areas. The proposed method and our findings are useful with respect to the application of nonlinear dynamics to investigate complex motions generated from granular materials.

Excitatory/inhibitory (E/I) balance is significantly associated with cognitive function. Its imbalance impairs cognitive function, particularly in patients with psychiatric disorders. Recent physiological and modeling findings show that excitatory postsynaptic potentials (EPSPs) have a long-tailed distribution and contribute to the generation of spontaneous activity. Moreover, this spontaneous activity and its response to the external stimulus significantly alternate under the different E/I balance. However, the effects of the E/I balance under long-tailed EPSPs at the functional level remain unknown. Hence, to elucidate this relationship, we constructed a reservoir computing (RC) model generating the long-tailed distribution of EPSPs and investigated the effect of the E/I balance on the learning performance of RC in the memory capacity (MC) task, which measures how correctly delayed input signals can be reproduced. The results revealed that an appropriate E/I balance maximized the MC. This high MC was realized by recurrent spike propagation under long-tailed EPSPs. These findings contribute to the understanding of the effect of the E/I balance in physiologically relevant neural networks.