We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data from chaotic chemical oscillators.

A widely held assumption on network dynamics is that similar components are more likely to exhibit similar behavior than dissimilar ones and that generic differences among them are necessarily detrimental to synchronization. Here, we show that this assumption does not generally hold in oscillator networks when communication delays are present. We demonstrate, in particular, that random parameter heterogeneity among oscillators can consistently rescue the system from losing synchrony. This finding is supported by electrochemical-oscillator experiments performed on a multielectrode array network. Remarkably, at intermediate levels of heterogeneity, random mismatches are more effective in promoting synchronization than parameter assignments specifically designed to facilitate identical synchronization. Our results suggest that, rather than being eliminated or ignored, intrinsic disorder in technological and biological systems can be harnessed to help maintain coherence required for function.

A phenomenological study of the mercury beating heart system in a three electrode electrochemical cell configuration forced with a harmonic perturbation is presented. The system is controlled via a potentiostat, where the mercury drop is electrically connected to a platinum wire and acts as the working electrode. This configuration exhibits geometrical shapes and complex surface structures when a harmonic signal is superimposed to the working electrode potential. This study involves a wide range of frequencies and amplitudes of the forcing signal. Differents levels of structure complexity are observed as a function of the parameters of the applied perturbation. At certain amplitudes and frequencies, rotational behavior is also observed.

NaClO3 is achiral in solution. If crystallization is performed under a static set‐up, it is recognized that the stochastic nucleation probability results in a racemic mixture of the conglomerate. In this paper, we report a reexamination of the crystallization of NaClO3 from static solution in petri dishes that was conducted over a number of years and is based on the count and analysis of several thousand d‐ vs. l‐NaClO3 crystals. Remarkably, instead of an expected nearly 50/50 coin‐tossing situation for the d/l crystal frequency, in most of our experiments a statistically significant bias in favor of d‐ over l‐NaClO3 crystals was found. The experiments also showed that the NaClO3 system was relatively insensitive regarding the intentional addition of a variety of optically active agents. Only in some cases, the persisting d‐bias observed in the unseeded experiments slightly increased upon the presence of such additives. Nevertheless, experiments in plastic petri dishes or in presence of fungal spores were able to reverse this bias. A literature survey shows that mainly d‐directed non‐stochastic behavior in the NaClO3 system has been previously observed in other laboratory settings and by the application of different crystallization techniques. So far, the kind of chiral influence that could be at the origin of the observed bias remains unknown. After the examination of several possible chiral influences of physical, chemical and biological origin, we carefully consider the presence of bio‐contaminants as most likely for the cause of this effect.

Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among oscillators, in spite that such models were originally defined as oscillator networks with pairwise interactions. Here, we show that hypernetworks can spontaneously emerge even in the presence of pairwise albeit nonlinear coupling given certain triplet frequency resonance conditions. The results are demonstrated in experiments with electrochemical oscillators and in simulations with integrate-and-fire neurons. By developing a comprehensive theory, we uncover the mechanism for emergent hypernetworks by identifying appearing and forbidden frequency resonant conditions. Furthermore, it is shown that microscopic linear (difference) coupling among units results in coupled mean fields, which have sufficient nonlinearity to facilitate hypernetworks. Our findings shed light on the apparent abundance of hypernetworks and provide a constructive way to predict and engineer their emergence.