Complex networks reveal global pattern of extreme-rainfall teleconnections.

Climatic observables are often correlated across long spatial distances, and extreme events, such as heatwaves or floods, are typically assumed to be related to such teleconnections1,2. Revealing atmospheric teleconnection patterns and understanding their underlying mechanisms is of great importance for weather forecasting in general and extreme-event prediction in particular3,4, especially considering that the characteristics of extreme events have been suggested to change under ongoing anthropogenic climate change5-8. Here we reveal the global coupling pattern of extreme-rainfall events by applying complex-network methodology to high-resolution satellite data and introducing a technique that corrects for multiple-comparison bias in functional networks. We find that the distance distribution of significant connections (P < 0.005) around the globe decays according to a power law up to distances of about 2,500 kilometres. For longer distances, the probability of significant connections is much higher than expected from the scaling of the power law. We attribute the shorter, power-law-distributed connections to regional weather systems. The longer, super-power-law-distributed connections form a global rainfall teleconnection pattern that is probably controlled by upper-level Rossby waves. We show that extreme-rainfall events in the monsoon systems of south-central Asia, east Asia and Africa are significantly synchronized. Moreover, we uncover concise links between south-central Asia and the European and North American extratropics, as well as the Southern Hemisphere extratropics. Analysis of the atmospheric conditions that lead to these teleconnections confirms Rossby waves as the physical mechanism underlying these global teleconnection patterns and emphasizes their crucial role in dynamical tropical-extratropical couplings. Our results provide insights into the function of Rossby waves in creating stable, global-scale dependencies of extreme-rainfall events, and into the potential predictability of associated natural hazards.

Network-based forecasting of climate phenomena.

Network theory, as emerging from complex systems science, can provide critical predictive power for mitigating the global warming crisis and other societal challenges. Here we discuss the main differences of this approach to classical numerical modeling and highlight several cases where the network approach substantially improved the prediction of high-impact phenomena: 1) El Niño events, 2) droughts in the central Amazon, 3) extreme rainfall in the eastern Central Andes, 4) the Indian summer monsoon, and 5) extreme stratospheric polar vortex states that influence the occurrence of wintertime cold spells in northern Eurasia. In this perspective, we argue that network-based approaches can gainfully complement numerical modeling.

Co-evolution of heterogeneous cognition in spatial snowdrift game with asymmetric cost.

The emergence of the evolutionary game on complex networks provides a fresh framework for studying cooperation behavior between complex populations. Numerous recent progress has been achieved in studying asymmetric games. However, there is still a substantial need to address how to flexibly express the individual asymmetric nature. In this paper, we employ mutual cognition among individuals to elucidate the asymmetry inherent in their interactions. Cognition arises from individuals' subjective assessments and significantly influences their decision-making processes. In social networks, mutual cognition among individuals is a persistent phenomenon and frequently displays heterogeneity as the influence of their interactions. This unequal cognitive dynamic will, in turn, influence the interactions, culminating in asymmetric outcomes. To better illustrate the inter-individual cognition in asymmetric snowdrift games, the concept of favor value is introduced here. On this basis, the evolution of cognition and its relationship with asymmetry degree are defined. In our simulation, we investigate how game cost and the intensity of individual cognitive changes impact the cooperation frequency. Furthermore, the temporal evolution of individual cognition and its variation under different parameters was also examined. The simulation results reveal that the emergence of heterogeneous cognition effectively addresses social dilemmas, with asymmetric interactions among individuals enhancing the propensity for cooperative choices. It is noteworthy that distinctions exist in the rules governing cooperation and cognitive evolution between regular networks and Watts-Strogatz small-world networks. In light of this, we deduce the relationship between cognition evolution and cooperative behavior in co-evolution and explore potential factors influencing cooperation within the system.

Deep learning-based state prediction of the Lorenz system with control parameters.

Nonlinear dynamical systems with control parameters may not be well modeled by shallow neural networks. In this paper, the stable fixed-point solutions, periodic and chaotic solutions of the parameter-dependent Lorenz system are learned simultaneously via a very deep neural network. The proposed deep learning model consists of a large number of identical linear layers, which provide excellent nonlinear mapping capability. Residual connections are applied to ease the flow of information and a large training dataset is further utilized. Extensive numerical results show that the chaotic solutions can be accurately forecasted for several Lyapunov times and long-term predictions are achieved for periodic solutions. Additionally, the dynamical characteristics such as bifurcation diagrams and largest Lyapunov exponents can be well recovered from the learned solutions. Finally, the principal factors contributing to the high prediction accuracy are discussed.

Recurrent chaotic clustering and slow chaos in adaptive networks.

Adaptive dynamical networks are network systems in which the structure co-evolves and interacts with the dynamical state of the nodes. We study an adaptive dynamical network in which the structure changes on a slower time scale relative to the fast dynamics of the nodes. We identify a phenomenon we refer to as recurrent adaptive chaotic clustering (RACC), in which chaos is observed on a slow time scale, while the fast time scale exhibits regular dynamics. Such slow chaos is further characterized by long (relative to the fast time scale) regimes of frequency clusters or frequency-synchronized dynamics, interrupted by fast jumps between these regimes. We also determine parameter values where the time intervals between jumps are chaotic and show that such a state is robust to changes in parameters and initial conditions.

SAMSGL: Series-aligned multi-scale graph learning for spatiotemporal forecasting.

Spatiotemporal forecasting in various domains, like traffic prediction and weather forecasting, is a challenging endeavor, primarily due to the difficulties in modeling propagation dynamics and capturing high-dimensional interactions among nodes. Despite the significant strides made by graph-based networks in spatiotemporal forecasting, there remain two pivotal factors closely related to forecasting performance that need further consideration: time delays in propagation dynamics and multi-scale high-dimensional interactions. In this work, we present a Series-Aligned Multi-Scale Graph Learning (SAMSGL) framework, aiming to enhance forecasting performance. In order to handle time delays in spatial interactions, we propose a series-aligned graph convolution layer to facilitate the aggregation of non-delayed graph signals, thereby mitigating the influence of time delays for the improvement in accuracy. To understand global and local spatiotemporal interactions, we develop a spatiotemporal architecture via multi-scale graph learning, which encompasses two essential components: multi-scale graph structure learning and graph-fully connected (Graph-FC) blocks. The multi-scale graph structure learning includes a global graph structure to learn both delayed and non-delayed node embeddings, as well as a local one to learn node variations influenced by neighboring factors. The Graph-FC blocks synergistically fuse spatial and temporal information to boost prediction accuracy. To evaluate the performance of SAMSGL, we conduct experiments on meteorological and traffic forecasting datasets, which demonstrate its effectiveness and superiority.

Synchronization enhancement subjected to adaptive blinking coupling.

Synchronization holds a significant role, notably within chaotic systems, in various contexts where the coordinated behavior of systems plays a pivotal and indispensable role. Hence, many studies have been dedicated to investigating the underlying mechanism of synchronization of chaotic systems. Networks with time-varying coupling, particularly those with blinking coupling, have been proven essential. The reason is that such coupling schemes introduce dynamic variations that enhance adaptability and robustness, making them applicable in various real-world scenarios. This paper introduces a novel adaptive blinking coupling, wherein the coupling adapts dynamically based on the most influential variable exhibiting the most significant average disparity. To ensure an equitable selection of the most effective coupling at each time instance, the average difference of each variable is normalized to the synchronous solution's range. Due to this adaptive coupling selection, synchronization enhancement is expected to be observed. This hypothesis is assessed within networks of identical systems, encompassing Lorenz, Rössler, Chen, Hindmarsh-Rose, forced Duffing, and forced van der Pol systems. The results demonstrated a substantial improvement in synchronization when employing adaptive blinking coupling, particularly when applying the normalization process.

Impact of periodic vaccination in SEIRS seasonal model.

We study three different strategies of vaccination in an SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) seasonal forced model, which are (i) continuous vaccination; (ii) periodic short-time localized vaccination, and (iii) periodic pulsed width campaign. Considering the first strategy, we obtain an expression for the basic reproduction number and infer a minimum vaccination rate necessary to ensure the stability of the disease-free equilibrium (DFE) solution. In the second strategy, short duration pulses are added to a constant baseline vaccination rate. The pulse is applied according to the seasonal forcing phases. The best outcome is obtained by locating intensive immunization at inflection of the transmissivity curve. Therefore, a vaccination rate of 44.4% of susceptible individuals is enough to ensure DFE. For the third vaccination proposal, additionally to the amplitude, the pulses have a prolonged time width. We obtain a non-linear relationship between vaccination rates and the duration of the campaign. Our simulations show that the baseline rates, as well as the pulse duration, can substantially improve the vaccination campaign effectiveness. These findings are in agreement with our analytical expression. We show a relationship between the vaccination parameters and the accumulated number of infected individuals, over the years, and show the relevance of the immunization campaign annual reaching for controlling the infection spreading. Regarding the dynamical behavior of the model, our simulations show that chaotic and periodic solutions as well as bi-stable regions depend on the vaccination parameters range.

Solvable Dynamics of Coupled High-Dimensional Generalized Limit-Cycle Oscillators.

We introduce a new model consisting of globally coupled high-dimensional generalized limit-cycle oscillators, which explicitly incorporates the role of amplitude dynamics of individual units in the collective dynamics. In the limit of weak coupling, our model reduces to the D-dimensional Kuramoto phase model, akin to a similar classic construction of the well-known Kuramoto phase model from weakly coupled two-dimensional limit-cycle oscillators. For the practically important case of D=3, the incoherence of the model is rigorously proved to be stable for negative coupling (K<0) but unstable for positive coupling (K>0); the locked states are shown to exist if K>0; in particular, the onset of amplitude death is theoretically predicted. For D≥2, the discrete and continuous spectra for both locked states and amplitude death are governed by two general formulas. Our proposed D-dimensional model is physically more reasonable, because it is no longer constrained by fixed amplitude dynamics, which puts the recent studies of the D-dimensional Kuramoto phase model on a stronger footing by providing a more general framework for D-dimensional limit-cycle oscillators.

Mechanisms of Photostimulation of Brain's Waste Disposal System: The Role of Singlet Oxygen.

There is strong evidence that augmentation of the brain's waste disposal system via stimulation of the meningeal lymphatics might be a promising therapeutic target for preventing neurological diseases. In our previous studies, we demonstrated activation of the brain's waste disposal system using transcranial photostimulation (PS) with a laser 1267 nm, which stimulates the direct generation of singlet oxygen in the brain tissues. Here we investigate the mechanisms underlying this phenomenon. Our results clearly demonstrate that PS-mediated stimulation of the brain's waste disposal system is accompanied by activation of lymphatic contractility associated with subsequent intracellular production of the reactive oxygen species and the nitric oxide underlying lymphatic relaxation. Thus, PS stimulates the brain's waste disposal system by influencing the mechanisms of regulation of lymphatic pumping.

Caring for the future can turn tragedy into comedy for long-term collective action under risk of collapse.

We will need collective action to avoid catastrophic climate change, and this will require valuing the long term as well as the short term. Shortsightedness and uncertainty have hindered progress in resolving this collective action problem and have been recognized as important barriers to cooperation among humans. Here, we propose a coupled social-ecological dilemma to investigate the interdependence of three well-identified components of this cooperation problem: 1) timescales of collapse and recovery in relation to time preferences regarding future outcomes, 2) the magnitude of the impact of collapse, and 3) the number of actors in the collective. We find that, under a sufficiently severe and time-distant collapse, how much the actors care for the future can transform the game from a tragedy of the commons into one of coordination, and even into a comedy of the commons in which cooperation dominates. Conversely, we also find conditions under which even strong concern for the future still does not transform the problem from tragedy to comedy. For a large number of participating actors, we find that the critical collapse impact, at which these game regime changes happen, converges to a fixed value of collapse impact per actor that is independent of the enhancement factor of the public good, which is usually regarded as the driver of the dilemma. Our results not only call for experimental testing but also help explain why polarization in beliefs about human-caused climate change can threaten global cooperation agreements.

Complexity-based approach for El Niño magnitude forecasting before the spring predictability barrier.

The El Niño Southern Oscillation (ENSO) is one of the most prominent interannual climate phenomena. Early and reliable ENSO forecasting remains a crucial goal, due to its serious implications for economy, society, and ecosystem. Despite the development of various dynamical and statistical prediction models in the recent decades, the "spring predictability barrier" remains a great challenge for long-lead-time (over 6 mo) forecasting. To overcome this barrier, here we develop an analysis tool, System Sample Entropy (SysSampEn), to measure the complexity (disorder) of the system composed of temperature anomaly time series in the Niño 3.4 region. When applying this tool to several near-surface air temperature and sea surface temperature datasets, we find that in all datasets a strong positive correlation exists between the magnitude of El Niño and the previous calendar year's SysSampEn (complexity). We show that this correlation allows us to forecast the magnitude of an El Niño with a prediction horizon of 1 y and high accuracy (i.e., root-mean-square error = 0.23° C for the average of the individual datasets forecasts). For the 2018 El Niño event, our method forecasted a weak El Niño with a magnitude of 1.11±0.23° C. Our framework presented here not only facilitates long-term forecasting of the El Niño magnitude but can potentially also be used as a measure for the complexity of other natural or engineering complex systems.

Communicating sentiment and outlook reverses inaction against collective risks.

Collective risks permeate society, triggering social dilemmas in which working toward a common goal is impeded by selfish interests. One such dilemma is mitigating runaway climate change. To study the social aspects of climate-change mitigation, we organized an experimental game and asked volunteer groups of three different sizes to invest toward a common mitigation goal. If investments reached a preset target, volunteers would avoid all consequences and convert their remaining capital into monetary payouts. In the opposite case, however, volunteers would lose all their capital with 50% probability. The dilemma was, therefore, whether to invest one's own capital or wait for others to step in. We find that communicating sentiment and outlook helps to resolve the dilemma by a fundamental shift in investment patterns. Groups in which communication is allowed invest persistently and hardly ever give up, even when their current investment deficits are substantial. The improved investment patterns are robust to group size, although larger groups are harder to coordinate, as evidenced by their overall lower success frequencies. A clustering algorithm reveals three behavioral types and shows that communication reduces the abundance of the free-riding type. Climate-change mitigation, however, is achieved mainly by cooperator and altruist types stepping up and increasing contributions as the failure looms. Meanwhile, contributions from free riders remain flat throughout the game. This reveals that the mechanisms behind avoiding collective risks depend on an interaction between behavioral type, communication, and timing.

Predicting climatic tipping points.

Increased levels of greenhouse gases in the atmosphere, especially carbon dioxide, are leading contributors to a significant increase in the global temperature, and the consequent global climatic changes are more noticeable in recent years than in the past. A persistent increased growth of such gases might lead to an irreversible transition or tipping of the Earth's climatic system to a new dynamical state. A change of regimes in CO 2 buildup being correlated to one in global climate patterns, predicting this tipping point becomes crucially important. We propose here an innovative conceptual model, which does just this. Using the idea of rate-induced bifurcations, we show that a sufficiently rapid change in the system parameters beyond a critical value tips the system over to a new dynamical state. Our model when applied to real-world data detects tipping points, enables calculation of tipping rates and predicts their future values, and identifies thresholds beyond which tipping occurs. The model well captures the growth in time of the total global atmospheric fossil-fuel CO 2 concentrations, identifying regime shift changes through measurable parameters and enabling prediction of future trends based on past data. Our model shows two distinct routes to tipping. We predict that with the present trend of variation of atmospheric greenhouse gas concentrations, the Earth's climatic system would move over to a new stable dynamical regime in the year 2022. We determine a limit of 10.62 GtC at the start of 2022 for global CO 2 emissions in order to avoid this tipping.

Extreme multistability in symmetrically coupled clocks.

Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We analyze a model for pendulum clocks coupled by springs and suspended on an oscillating base and show how EM can be induced in this system by specifically designed coupling. First, we uncover that symmetric coupling can increase the dynamical complexity. In particular, the coexistence of multiple isolated attractors and continuous families of stable periodic states is generated in a symmetric cross-coupling scheme of four pendulums. These coexisting infinitely many states are characterized by different levels of phase synchronization between the pendulums, including anti-phase and in-phase states. Some of the states are characterized by splitting of the pendulums into groups with silent sub-threshold and oscillating behavior, respectively. The analysis of the basins of attraction further reveals the complex dependence of EM on initial conditions.

Asymmetry induces critical desynchronization of power grids.

Dynamical stability of the synchronous regime remains a challenging problem for secure functioning of power grids. Based on the symmetric circular model [Hellmann et al., Nat. Commun. 11, 592 (2020)], we demonstrate that the grid stability can be destroyed by elementary violations (motifs) of the network architecture, such as cutting a connection between any two nodes or removing a generator or a consumer. We describe the mechanism for the cascading failure in each of the damaging case and show that the desynchronization starts with the frequency deviation of the neighboring grid elements followed by the cascading splitting of the others, distant elements, and ending eventually in the bi-modal or a partially desynchronized state. Our findings reveal that symmetric topology underlines stability of the power grids, while local damaging can cause a fatal blackout.

Synchronization stability and multi-timescale analysis of renewable-dominated power systems.

Synchronization is one of the key issues in three-phase AC power systems. Its characteristics have been dramatically changed with the large-scale integration of power-electronic-based renewable energy, mainly including a permanent magnetic synchronous generator (PMSG) and a double-fed induction generator (DFIG) for wind energy and a photovoltaic (PV) generator for solar energy. In this paper, we review recent progresses on the synchronization stability and multi-timescale properties of the renewable-dominated power system (RDPS), from nodes and network perspectives. All PMSG, DFIG, and PV are studied. In the traditional synchronous generator (SG) dominated power system, its dynamics can be described by the differential-algebraic equations (DAEs), where the dynamic apparatuses are modeled by differential equations and the stationary networks are described by algebraic equations. Unlike the single electromechanical timescale and DAE description for the SG-dominated power system, the RDPS dynamics should be described by the multiscale dynamics of both nodes and networks. For three different timescales, including the AC current control, DC voltage control, and rotor electromechanical timescales, their corresponding models are well established. In addition, for the multiscale network dynamics, the dynamical network within the AC current control timescale, which should be described by differential equations, can also be simplified as algebraic equations. Thus, the RDPS dynamics can be put into a similar DAE diagram for each timescale to the traditional power system dynamics, with which most of power electrical engineers are familiar. It is also found that the phase-locked loop for synchronization plays a crucial role in the whole system dynamics. The differences in the synchronization and multiscale characteristics between the traditional power system and the RDPS are well uncovered and summarized. Therefore, the merit of this paper is to establish a basic physical picture for the stability mechanism in the RDPS, which still lacks systematic studies and is controversial in the field of electrical power engineering.

Symbiosis of an artificial neural network and models of biological neurons: Training and testing.

In this paper, we show the possibility of creating and identifying the features of an artificial neural network (ANN), which consists of mathematical models of biological neurons. The FitzHugh-Nagumo (FHN) system is used as a paradigmatic model demonstrating basic neuron activities. First, in order to reveal how biological neurons can be embedded within an ANN, we train the ANN with nonlinear neurons to solve a basic image recognition problem with an MNIST database; next, we describe how FHN systems can be introduced into this trained ANN. After all, we show that an ANN with FHN systems inside can be successfully trained with improved accuracy comparing with first trained ANN and then with inserted FHN systems. This approach opens up great opportunities in terms of the direction of analog neural networks, in which artificial neurons can be replaced by more appropriate biological ones.

Interconnected ordinal pattern complex network for characterizing the spatial coupling behavior of gas-liquid two-phase flow.

The complex phase interactions of the two-phase flow are a key factor in understanding the flow pattern evolutional mechanisms, yet these complex flow behaviors have not been well understood. In this paper, we employ a series of gas-liquid two-phase flow multivariate fluctuation signals as observations and propose a novel interconnected ordinal pattern network to investigate the spatial coupling behaviors of the gas-liquid two-phase flow patterns. In addition, we use two network indices, which are the global subnetwork mutual information (I) and the global subnetwork clustering coefficient (C), to quantitatively measure the spatial coupling strength of different gas-liquid flow patterns. The gas-liquid two-phase flow pattern evolutionary behaviors are further characterized by calculating the two proposed coupling indices under different flow conditions. The proposed interconnected ordinal pattern network provides a novel tool for a deeper understanding of the evolutional mechanisms of the multi-phase flow system, and it can also be used to investigate the coupling behaviors of other complex systems with multiple observations.

Synchronization stability of power-grid-tied converters.

Synchronization stability is one of central problems in power systems, and it is becoming much more complicated with the high penetration of renewable energy and power electronics devices. In this paper, we review recent work by several nonlinear models for renewable-dominated power systems in terms of multiple timescales, in particular, grid-tied converters within the DC voltage timescale. For the simplest model, a second-order differential equations called the generalized swing equation by considering only the phase-locked loop (PLL) is obtained, which shows a similar form with the well-known swing equation for a synchronous generator in the traditional power systems. With more outer controllers included, fourth-order and fifth-order models can be obtained. The fourth-order model is called the extended generalized swing equation, exhibiting the combined function of grid synchronization and active power balance on the DC capacitor. In addition, a nonlinear model for a two coupled converter system is given. Based on these studies, we find that the PLL plays a key role in synchronization stability. In summary, the value of this paper is to clarify the key concept of the synchronization stability in renewable-dominated power systems based on different nonlinear models, which still lacks systematic studies and is controversial in the field of electrical power engineering. Meanwhile, it clearly uncovers that the synchronization stability of converters has its root in the phase synchronization concept in nonlinear sciences.