Characterizing the spike timing of a chaotic laser by using ordinal analysis and machine learning.

Semiconductor lasers with optical feedback are well-known nonlinear dynamical systems. Under appropriate feedback conditions, these lasers emit optical pulses that resemble neural spikes. Influenced by feedback delay and various noise sources, including quantum spontaneous emission noise, the dynamics are highly stochastic. A good understanding of the spike timing statistics is needed to develop photonic systems capable of using the fast-spiking laser output for novel applications, such as information processing or random number generation. Here we analyze experimental sequences of inter-spike intervals (ISIs) recorded when a sinusoidal signal was applied to the laser current. Different combinations of the DC value and frequency of the signal applied to the laser lead to ISI sequences with distinct statistical properties. This variability prompts an investigation into the relationship between experimental parameters and ISI sequence statistics, aiming to uncover potential encoding methods for optical spikes, since this can open a new way of encoding and decoding information in sequences of optical spikes. By using ordinal analysis and machine learning, we show that the ISI sequences have statistical ordinal properties that are similar to Flicker noise signals, characterized by a parameter α that varies with the signal that was applied to the laser current when the ISIs were recorded. We also show that for this dataset, the (α, permutation entropy) plane is more informative than the (complexity, permutation entropy) plane because it allows better differentiation of ISI sequences recorded under different experimental conditions, as well as better differentiation of original and surrogate ISI sequences.

Power-grid vulnerability and its relation with network structure.

Interconnected systems with critical infrastructures can be affected by small failures that may trigger a large-scale cascade of failures, such as blackouts in power grids. Vulnerability indices provide quantitative measures of a network resilience to component failures, assessing the break of information or energy flow in a system. Here, we focus on a network vulnerability analysis, that is, indices based solely on the network structure and its static characteristics, which are reliably available for most complex networks. This work studies the structural connectivity of power grids, assessing the main centrality measures in network science to identify vulnerable components (transmission lines or edges) to attacks and failures. Specifically, we consider centrality measures that implicitly model the power flow distribution in power systems. This framework allow us to show that the efficiency of the power flow in a grid can be highly sensitive to attacks on specific (central) edges. Numerical results are presented for randomly generated power-grid models and established power-grid benchmarks, where we demonstrate that the system's energy efficiency is more vulnerable to attacks on edges that are central to the power flow distribution. We expect that the vulnerability indices investigated in our work can be used to guide the design of structurally resilient power grids.

Phase synchronization in a sparse network of randomly connected neurons under the effect of Poissonian spike inputs.

This article investigates the emergence of phase synchronization in a network of randomly connected neurons by chemical synapses. The study uses the classic Hodgkin-Huxley model to simulate the neuronal dynamics under the action of a train of Poissonian spikes. In such a scenario, we observed the emergence of irregular spikes for a specific range of conductances and also that the phase synchronization of the neurons is reached when the external current is strong enough to induce spiking activity but without overcoming the coupling current. Conversely, if the external current assumes very high values, then an opposite effect is observed, i.e., the prevention of the network synchronization. We explain such behaviors considering different mechanisms involved in the system, such as incoherence, minimization of currents, and stochastic effects from the Poissonian spikes. Furthermore, we present some numerical simulations where the stimulation of only a fraction of neurons, for instance, can induce phase synchronization in the non-stimulated fraction of the network, besides cases in which for larger coupling values, it is possible to propagate the spiking activity in the network when considering stimulation over only one neuron.

How heterogeneity in connections and cycles matter for synchronization of complex networks.

We analyze how the structure of complex networks of non-identical oscillators influences synchronization in the context of the Kuramoto model. The complex network metrics assortativity and clustering coefficient are used in order to generate network topologies of Erdös-Rényi, Watts-Strogatz, and Barabási-Albert types that present high, intermediate, and low values of these metrics. We also employ the total dissonance metric for neighborhood similarity, which generalizes to networks the standard concept of dissonance between two non-identical coupled oscillators. Based on this quantifier and using an optimization algorithm, we generate Similar, Dissimilar, and Neutral natural frequency patterns, which correspond to small, large, and intermediate values of total dissonance, respectively. The emergency of synchronization is numerically studied by considering these three types of dissonance patterns along with the network topologies generated by high, intermediate, and low values of the metrics assortativity and clustering coefficient. We find that, in general, low values of these metrics appear to favor phase locking, especially for the Similar dissonance pattern.

Synchronization in populations of electrochemical bursting oscillators with chaotic slow dynamics.

We investigate the synchronization of coupled electrochemical bursting oscillators using the electrodissolution of iron in sulfuric acid. The dynamics of a single oscillator consisted of slow chaotic oscillations interrupted by a burst of fast spiking, generating a multiple time-scale dynamical system. A wavelet analysis first decomposed the time series data from each oscillator into a fast and a slow component, and the corresponding phases were also obtained. The phase synchronization of the fast and slow dynamics was analyzed as a function of electrical coupling imposed by an external coupling resistance. For two oscillators, a progressive transition was observed: With increasing coupling strength, first, the fast bursting intervals overlapped, which was followed by synchronization of the fast spiking, and finally, the slow chaotic oscillations synchronized. With a population of globally coupled 25 oscillators, the coupling eliminated the fast dynamics, and only the synchronization of the slow dynamics can be observed. The results demonstrated the complexities of synchronization with bursting oscillations that could be useful in other systems with multiple time-scale dynamics, in particular, in neuronal networks.

Uncovering episodic influence of oceans on extreme drought events in Northeast Brazil by ordinal partition network approaches.

Since 2012, the semiarid region of Northeast Brazil (NEB) has been experiencing a continuous dry condition imposing significant social impacts and economic losses. Characterizing the recent extreme drought events and uncovering the influence from the surrounding oceans remain to be big challenges. The physical mechanisms of extreme drought events in the NEB are due to varying interacting time scales from the surrounding tropical oceans (Pacific and Atlantic). From time series observations, we propose a three-step strategy to establish the episodic coupling directions on intraseasonal time scales from the ocean to the precipitation patterns in the NEB, focusing on the distinctive roles of the oceans during the recent extreme drought events of 2012-2013 and 2015-2016. Our algorithm involves the following: (i) computing drought period length from daily precipitation anomalies to capture extreme drought events; (ii) characterizing the episodic coupling delays from the surrounding oceans to the precipitation by applying the Kullback-Leibler divergence (KLD) of complexity measure, which is based on ordinal partition transition network representation of time series; and (iii) calculating the ratio of high temperature in the ocean during the extreme drought events with proper time lags that are identified by KLD measures. From the viewpoint of climatology, our analysis provides data-based evidence of showing significant influence from the North Atlantic in 2012-2013 to the NEB, but in 2015-2016, the Pacific played a dominant role than that of the Atlantic. The episodic intraseasonal time scale properties are potential for monitoring and forecasting droughts in the NEB in order to propose strategies for drought impacts reduction.

Extraction of slow and fast dynamics of multiple time scale systems using wavelet techniques.

A methodology is presented based on wavelet techniques to approximate fast and slow dynamics present in time-series whose behavior is characterized by different local scales in time. These approximations are useful to understand the global dynamics of the original full systems, especially in experimental situations where all information is contained in a one-dimensional time-series. Wavelet analysis is a natural approach to handle these approximations because each dynamical behavior manifests its specific subset in frequency domain, for example, with two time scales, the slow and fast dynamics, present in low and high frequencies, respectively. The proposed procedure is illustrated by the analysis of a complex experimental time-series of iron electrodissolution where the slow chaotic dynamics is interrupted by fast irregular spiking. The method can be used to first filter the time-series data and then separate the fast and slow dynamics even when clear maxima and/or minima in the corresponding global wavelet spectrum are missing. The results could find applications in the analysis of synchronization of complex systems through multi-scale analysis.

Experimental phase synchronization detection in non-phase coherent chaotic systems by using the discrete complex wavelet approach.

Phase synchronization may emerge from mutually interacting non-linear oscillators, even under weak coupling, when phase differences are bounded, while amplitudes remain uncorrelated. However, the detection of this phenomenon can be a challenging problem to tackle. In this work, we apply the Discrete Complex Wavelet Approach (DCWA) for phase assignment, considering signals from coupled chaotic systems and experimental data. The DCWA is based on the Dual-Tree Complex Wavelet Transform (DT-CWT), which is a discrete transformation. Due to its multi-scale properties in the context of phase characterization, it is possible to obtain very good results from scalar time series, even with non-phase-coherent chaotic systems without state space reconstruction or pre-processing. The method correctly predicts the phase synchronization for a chemical experiment with three locally coupled, non-phase-coherent chaotic processes. The impact of different time-scales is demonstrated on the synchronization process that outlines the advantages of DCWA for analysis of experimental data.

Star-type oscillatory networks with generic Kuramoto-type coupling: A model for "Japanese drums synchrony".

We analyze star-type networks of phase oscillators by virtue of two methods. For identical oscillators we adopt the Watanabe-Strogatz approach, which gives full analytical description of states, rotating with constant frequency. For nonidentical oscillators, such states can be obtained by virtue of the self-consistent approach in a parametric form. In this case stability analysis cannot be performed, however with the help of direct numerical simulations we show which solutions are stable and which not. We consider this system as a model for a drum orchestra, where we assume that the drummers follow the signal of the leader without listening to each other and the coupling parameters are determined by a geometrical organization of the orchestra.

The discrete complex wavelet approach to phase assignment and a new test bed for related methods.

A new approach based on the dual-tree complex wavelet transform is introduced for phase assignment to non-linear oscillators, namely, the Discrete Complex Wavelet Approach-DCWA. This methodology is able to measure phase difference with enough accuracy to track fine variations, even in the presence of Gaussian observational noise and when only a single scalar measure of the oscillator is available. So, it can be an especially interesting tool to deal with experimental data. In order to compare it with other phase detection techniques, a testbed is introduced. This testbed provides time series from dynamics similar to non-linear oscillators, such that a theoretical phase choice is known in advance. Moreover, it allows to tune different types of phase synchronization to test phase detection methods under a variety of scenarios. Through numerical benchmarks, we report that the proposed approach is a reliable alternative and that it is particularly effective compared with other methodologies in the presence of moderate to large noises.

Synchronization of oscillators in a Kuramoto-type model with generic coupling.

We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of oscillators to the mean field and to different forces from the mean field on oscillators. We present the explicit solutions of self-consistency equations for the amplitude and frequency of the mean field in a parametric form, valid for noise-free and noise-driven oscillators. As an example, we consider spatially spreaded oscillators for which the coupling properties are determined by finite velocity of signal propagation.

Unravelling COVID-19 waves in Rio de Janeiro city: Qualitative insights from nonlinear dynamic analysis.

Since the COVID-19 pandemic was first reported in 2019, it has rapidly spread around the world. Many countries implemented several measures to try to control the virus spreading. The healthcare system and consequently the general quality of life population in the cities have all been significantly impacted by the Coronavirus pandemic. The different waves of contagious were responsible for the increase in the number of cases that, unfortunately, many times lead to death. In this paper, we aim to characterize the dynamics of the six waves of cases and deaths caused by COVID-19 in Rio de Janeiro city using techniques such as the Poincaré plot, approximate entropy, second-order difference plot, and central tendency measures. Our results reveal that by examining the structure and patterns of the time series, using a set of non-linear techniques we can gain a better understanding of the role of multiple waves of COVID-19, also, we can identify underlying dynamics of disease spreading and extract meaningful information about the dynamical behavior of epidemiological time series. Such findings can help to closely approximate the dynamics of virus spread and obtain a correlation between the different stages of the disease, allowing us to identify and categorize the stages due to different virus variants that are reflected in the time series.

Adaptive node-to-node pinning synchronization control of complex networks.

In this work, we propose an adaptive node-to-node pinning control strategy. In this approach, both the coupling strength among nodes and the pinning control gains are adaptively changed according to well chosen adaptation laws that take into account the specificities of the oscillators and the network topology. Proof of stability and performance comparison is also shown in this paper.

Basin sizes depend on stable eigenvalues in the Kuramoto model.

We show that for the Kuramoto model (with identical phase oscillators equally coupled), its global statistics and size of the basins of attraction can be estimated through the eigenvalues of all stable (frequency) synchronized states. This result is somehow unexpected since, by doing that, one could just use a local analysis to obtain the global dynamic properties. But recent works based on Koopman and Perron-Frobenius operators demonstrate that the global features of a nonlinear dynamical system, with some specific conditions, are somehow encoded in the local eigenvalues of its equilibrium states. Recognized numerical simulations in the literature reinforce our analytical results.

Characterisation of neonatal cardiac dynamics using ordinal partition network.

The maturation of the autonomic nervous system (ANS) starts in the gestation period and it is completed after birth in a variable time, reaching its peak in adulthood. However, the development of ANS maturation is not entirely understood in newborns. Clinically, the ANS condition is evaluated with monitoring of gestational age, Apgar score, heart rate, and by quantification of heart rate variability using linear methods. Few researchers have addressed this problem from the perspective nonlinear data analysis. This paper proposes a new data-driven methodology using nonlinear time series analysis, based on complex networks, to classify ANS conditions in newborns. We map 74 time series given by RR intervals from premature and full-term newborns to ordinal partition networks and use complexity quantifiers to discriminate the dynamical process present in both conditions. We obtain three complexity quantifiers (permutation, conditional, and global node entropies) using network mappings from forward and reverse directions, and considering different time lags and embedding dimensions. The results indicate that time asymmetry is present in the data of both groups and the complexity quantifiers can differentiate the groups analysed. We show that the conditional and global node entropies are sensitive for detecting subtle differences between the neonates, particularly for small embedding dimensions (m < 7). This study reinforces the assessment of nonlinear techniques for RR interval time series analysis. Graphical Abstract.

epidWaves: A code for fitting multi-wave epidemic models.

The COVID-19 pandemic has given rise to a great demand for computational models capable of describing and inferring the evolution of an epidemic outbreak in the short term. In this sense, we introduce epidWaves, a package that provides a framework for fitting multi-wave epidemic models to data from actual outbreaks of COVID-19 and other infectious diseases.

Topological indexes and community structure for urban mobility networks: Variations in a business day.

Topological analysis and community detection in mobility complex networks have an essential role in many contexts, from economics to the environmental agenda. However, in many cases, the dynamic component of mobility data is not considered directly. In this paper, we study how topological indexes and community structure changes in a business day. For the analyzes, we use a mobility database with a high temporal resolution. Our case study is the city of São José dos Campos (Brazil)-the city is divided into 55 traffic zones. More than 20 thousand people were asked about their travels the day before the survey (Origin-Destination Survey). We generated a set of graphs, where each vertex represents a traffic zone, and the edges are weighted by the number of trips between them, restricted to a time window. We calculated topological properties, such as degree, clustering coefficient and diameter, and the network's community structure. The results show spatially concise community structures related to geographical factors such as highways and the persistence of some communities for different timestamps. These analyses may support the definition and adjustment of public policies to improve urban mobility. For instance, the community structure of the network might be useful for defining inter-zone public transportation.

Spatiotemporal data analysis with chronological networks.

The number of spatiotemporal data sets has increased rapidly in the last years, which demands robust and fast methods to extract information from this kind of data. Here, we propose a network-based model, called Chronnet, for spatiotemporal data analysis. The network construction process consists of dividing a geometric space into grid cells represented by nodes connected chronologically. Strong links in the network represent consecutive recurrent events between cells. The chronnet construction process is fast, making the model suitable to process large data sets. Using artificial and real data sets, we show how chronnets can capture data properties beyond simple statistics, like frequent patterns, spatial changes, outliers, and spatiotemporal clusters. Therefore, we conclude that chronnets represent a robust tool for the analysis of spatiotemporal data sets.

Bouncing ball problem: stability of the periodic modes.

Exploring all its ramifications, we give an overview of the simple yet fundamental bouncing ball problem, which consists of a ball bouncing vertically on a sinusoidally vibrating table under the action of gravity. The dynamics is modeled on the basis of a discrete map of difference equations, which numerically solved fully reveals a rich variety of nonlinear behaviors, encompassing irregular nonperiodic orbits, subharmonic and chaotic motions, chattering mechanisms, and also unbounded nonperiodic orbits. For periodic motions, the corresponding conditions for stability and bifurcation are determined from analytical considerations of a reduced map. Through numerical examples, it is shown that a slight change in the initial conditions makes the ball motion switch from periodic to chaotic orbits bounded by a velocity strip v=+/-Gamma(1-epsilon) , where Gamma is the nondimensionalized shaking acceleration and epsilon the coefficient of restitution which quantifies the amount of energy lost in the ball-table collision.

Bistable Firing Pattern in a Neural Network Model.

Excessively high, neural synchronization has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronization mechanisms can thus help control or even treat epilepsy. In this paper, we study neural synchronization in a random network where nodes are neurons with excitatory and inhibitory synapses, and neural activity for each node is provided by the adaptive exponential integrate-and-fire model. In this framework, we verify that the decrease in the influence of inhibition can generate synchronization originating from a pattern of desynchronized spikes. The transition from desynchronous spikes to synchronous bursts of activity, induced by varying the synaptic coupling, emerges in a hysteresis loop due to bistability where abnormal (excessively high synchronous) regimes exist. We verify that, for parameters in the bistability regime, a square current pulse can trigger excessively high (abnormal) synchronization, a process that can reproduce features of epileptic seizures. Then, we show that it is possible to suppress such abnormal synchronization by applying a small-amplitude external current on > 10% of the neurons in the network. Our results demonstrate that external electrical stimulation not only can trigger synchronous behavior, but more importantly, it can be used as a means to reduce abnormal synchronization and thus, control or treat effectively epileptic seizures.