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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. [ABSTRACT FROM AUTHOR]

The Edward N. Lorenz Early Career Award was given to three young researchers for their outstanding papers published in Chaos in 2022. The winners are Tiemo Pedergnana from ETH Zurich, Thomas Lilienkamp from Nuremberg Institute of Technology, and Yuzuru Kato from the University of Tokyo. Each winner will receive a $2000 honorarium and is invited to contribute a perspective article to the journal. The winning papers cover topics such as seeking hidden exact potentials in dynamical systems, developing low-energy defibrillation strategies for cardiac arrhythmias, and defining an asymptotic phase function for quantum nonlinear oscillators. The authors were eligible for the award if they received their Ph.D. within the past five years, their master's degree within the past eight years, or if they are current students. [Extracted from the article]

We report the discovery of two types of stability rings in the control parameter space of a vertical-cavity surface-emitting semiconductor laser. Stability rings are closed parameter paths in the laser control space. Inside such rings, laser stability thrives even in the presence of small parameter fluctuations. Stability rings were also found in rather distinct contexts, namely, in the way that cancerous, normal, and effector cells interact under ionizing radiation and in oscillations of an electronic circuit with a junction-gate field-effect transistor (JFET) diode. We argue that stability-enhancing rings are generic structures present in the control parameter space of many complex systems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We performed a scientometric analysis of Chaos papers from 1991 to 2019, applying a careful disambiguation process for identifying the authors correctly. First, we used standard scientometric tools based on descriptive statistics. This analysis enabled us to compute productivity and the degree of collaboration. The evolution in the number of authors, countries, and topics per article has an increasing trend. An analysis of the citations considering their temporal mean number exhibits a growing tendency in time. Second, we dealt with Lotka–Zipf's law considering the rank distributions of 15 datasets. We found that the sum of Crossref citations by country was the only dataset for which the power-law was the only plausible distribution. Next, we examined the networks of authors, countries, and topics, going from the simplest case of undirected and unweighted networks to the general case of weighted and directed networks and assigning a weight to the individual nodes. Based on the networks' topology and features, we introduced diversity, collaboration, influence, and productivity measures and found a significant increase in the diversity of all the considered networks (authors, countries, and topics) but manifesting a very different network structure. The computation of typical network quantities combined with the communities' identification reveals the presence of several hubs and the existence of various communities that encompass nodes of all the continents in the case of countries. Finally, using the most general networks, it was possible to compute influence and productivity indexes to find the USA, China, and Germany's leadership inside the network. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editors discuss various topics within the issue, including coupled Stuart-Landau oscillators, social tipping, and rate-induced tipping in spatially coupled ecological system.

Machine learning (ML), a subset of artificial intelligence, refers to methods that have the ability to "learn" from experience, enabling them to carry out designated tasks. The main focus of this Focus Issue is on the new algorithms, strategies, and techniques with machine learning applied to complex systems and on applying complex system techniques to leverage the performance of machine learning techniques with high-efficiency. Prediction and manipulations of complex systems Machine Learning (ML) algorithms have provided great convenience in terms of analyzing and predicting the dynamics of chaotic and complex systems. [Extracted from the article]

Many high-dimensional complex systems exhibit an enormously complex landscape of possible asymptotic states. Here, we present a numerical approach geared towards analyzing such systems. It is situated between the classical analysis with macroscopic order parameters and a more thorough, detailed bifurcation analysis. With our machine learning method, based on random sampling and clustering methods, we are able to characterize the different asymptotic states or classes thereof and even their basins of attraction. In order to do this, suitable, easy to compute, statistics of trajectories with randomly generated initial conditions and parameters are clustered by an algorithm such as DBSCAN. Due to its modular and flexible nature, our method has a wide range of possible applications in many disciplines. While typical applications are oscillator networks, it is not limited only to ordinary differential equation systems, every complex system yielding trajectories, such as maps or agent-based models, can be analyzed, as we show by applying it the Dodds–Watts model, a generalized SIRS-model, modeling social and biological contagion. A second order Kuramoto model, used, e.g. to investigate power grid dynamics, and a Stuart–Landau oscillator network, each exhibiting a complex multistable regime, are shown as well. The method is available to use as a package for the Julia language. [ABSTRACT FROM AUTHOR]

We propose a novel type of neural networks known as "attention-based sequence-to-sequence architecture" for a model-free prediction of spatiotemporal systems. This architecture is composed of an encoder and a decoder in which the encoder acts upon a given input sequence and then the decoder yields another output sequence to make a multistep prediction at a time. In order to demonstrate the potential of this approach, we train the neural network using data numerically sampled from the Korteweg–de Vries equation—which describes the interaction between solitary waves—and then predict its future evolution. Furthermore, we validate the applicability of the approach on datasets sampled from the chaotic Lorenz system and three other partial differential equations. The results show that the proposed method can achieve good performance in predicting the evolutionary behavior of studied spatiotemporal dynamics. To the best of our knowledge, this work is the first attempt at applying attention-based sequence-to-sequence architecture to the prediction task of solitary waves. [ABSTRACT FROM AUTHOR]

The following topical experts served as referees for papers submitted to I Chaos i during 2019. Leeuwen, Peter Jan Van Todd, Mike Zaks, Michael Zhang, Dan. [Extracted from the article]

Abstract In this paper, we are concerned with input-to-state stability of a class of memristive bidirectional associative memory (BAM) neural networks with variable time delays. Based on a nonsmooth analysis and set-valued maps, some novel sufficient conditions are obtained for the input-to-state stability of such networks, which extended some known results as particular cases. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of our results. Highlights • A class of general BAM neural networks with variable time delays are proposed compared with classical neural networks with constant synapse. • Some novel sufficient conditions are obtained for the input-to-state stability of such networks, which extended some known results. • The effect of variable time delays and constant time delays is compared based on our results. • The method from single-layer neural networks is extended to double-layer neural networks. [ABSTRACT FROM AUTHOR]

We propose a hybrid multiscale coarse-grained (HMCG) method which combines a fine Monte Carlo (MC) simulation on the part of nodes of interest with a more coarse Langevin dynamics on the rest part. We demonstrate the validity of our method by analyzing the equilibrium Ising model and the nonequilibrium susceptible-infected-susceptible model. It is found that HMCG not only works very well in reproducing the phase transitions and critical phenomena of the microscopic models, but also accelerates the evaluation of dynamics with significant computational savings compared to microscopic MC simulations directly for the whole networks. The proposed method is general and can be applied to a wide variety of networked systems just adopting appropriate microscopic simulation methods and coarse graining approaches. [ABSTRACT FROM AUTHOR]

The climate of South America exhibits pronounced differences between rainy and dry seasons, associated with specific synoptic features such as the establishment of the South Atlantic convergence zone. Here, we analyze the spatiotemporal correlation structure and in particular teleconnections of daily rainfall associated with these features by means of evolving complex networks. A modification of Pearson’s correlation coefficient is introduced to handle the intricate statistical properties of daily rainfall. On this basis, spatial correlation networks are constructed, and new appropriate network measures are introduced in order to analyze the temporal evolution of the networks’ characteristics. We particularly focus on the identification of coherent areas of similar rainfall patterns and previously unknown teleconnection structures between remote areas. We show that the monsoon onset is characterized by an abrupt transition from erratic to organized regional connectivity that prevails during the monsoon season, while only the onset times themselves exhibit anomalous large-scale organization of teleconnections. Furthermore, we reveal that the two mega-droughts in the Amazon basin were already announced in the previous year by an anomalous behavior of the connectivity structure. [ABSTRACT FROM AUTHOR]

Power grids and their properties have been studied broadly in many aspects. In this paper, we propose a novel concept, power-flow-based power grid, as a typical power-functional network, based on the calculation of power flow distribution from power electrical engineering. We compare it with structural networks based on the shortest path length and effective networks based on the effective electrical distance and study the relationship among these three kinds of networks. We find that they have roughly positive correlations with each other, indicating that in general any close nodes in the topological structure are actually connected in function. However, we do observe some counter- examples that two close nodes in a structural network can have a long distance in a power-functional network, namely, two physically connected nodes can actually be separated in function. In addition, we find that power grids in the structural network tend to be heterogeneous, whereas those in the effective and power-functional networks tend to be homogeneous. These findings are expected to be significant not only for power grids but also for various other complex networks. [ABSTRACT FROM AUTHOR]

• We propose a temporal network model considering the stochastic phase transition of vertices. • Theoretical analysis is derived based on the continuous Markov chain method and confirmed by simulations. • Application in fitting the real network is discussed. Complex networks have played an important role in describing real complex systems since the end of the last century. Recently, research on real-world data sets reports intermittent interaction among social individuals. In this paper, we pay attention to this typical phenomenon of intermittent interaction by considering the state transition of network vertices between online and hidden based on the birth and death process. By continuous-time Markov theory, we show that both the number of each vertex's online neighbors and the online network size are stable and follow the homogeneous probability distribution in a similar form, inducing similar statistics as well. In addition, all propositions are verified via simulations. Moreover, we also present the degree distributions based on small-world and scale-free networks and find some regular patterns by simulations. The application in fitting real networks is discussed. [ABSTRACT FROM AUTHOR]

Electronic circuits are useful tools for studying potential dynamical behaviors of synthetic genetic networks. The circuit models are complementary to numerical simulations of the networks, especially providing a framework for verification of dynamical behaviors in the presence of intrinsic and extrinsic noise of the electrical systems. Here we present an improved version of our previous design of an electronic analog of genetic networks that includes the 3-gene Repressilator and we show conversions between model parameters and real circuit component values to mimic the numerical results in experiments. Important features of the circuit design include the incorporation of chemical kinetics representing Hill function inhibition, quorum sensing coupling, and additive noise. Especially, we make a circuit design for a systematic change of initial conditions in experiment, which is critically important for studies of dynamical systems' behavior, particularly, when it shows multistability. This improved electronic analog of the synthetic genetic network allows us to extend our investigations from an isolated Repressilator to coupled Repressilators and to reveal the dynamical behavior's complexity. [ABSTRACT FROM AUTHOR]

We study how the phenomenon of response to synchronization arises in sets of pulse-coupled dissimilar oscillators. One of the sets is constituted by oscillators that can easily synchronize. Conversely, the oscillators of the other set do not synchronize. When the elements of the first set are not synchronized, they induce oscillation death in the constituents of the second set. By contrast, when synchronization is achieved in oscillators of the first set, those of the second set recover their oscillatory behavior and thus, responding to synchronization. Additionally, we found another interesting phenomenon in this type of systems, namely, a new control of simultaneous firings in a population of similar oscillators attained by means of the action of a dissimilar oscillator. [ABSTRACT FROM AUTHOR]

We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks. [ABSTRACT FROM AUTHOR]

We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development of complex systems analysis. First, we discuss the transforming of a time series from such systems to a complex network. The natural approach is to calculate the recurrence matrix and interpret such as the adjacency matrix of an associated complex network, called recurrence network. Using complex network measures, such as transitivity coefficient, we demonstrate that this approach is very efficient for identifying qualitative transitions in observational data, e.g., when analyzing paleoclimate regime transitions. Second, we demonstrate the use of directed spatial networks constructed from spatio-temporal measurements of such systems that can be derived from the synchronized-in-time occurrence of extreme events in different spatial regions. Although there are many possibilities to investigate such spatial networks, we present here the new measure of network divergence and how it can be used to develop a prediction scheme of extreme rainfall events. [ABSTRACT FROM AUTHOR]

Heterogeneity among interacting units plays an important role in numerous biological and man-made complex systems. While the impacts of heterogeneity on synchronization, in terms of structural mismatch of the layers in multiplex networks, has been studied thoroughly, its influence on intralayer synchronization, in terms of parameter mismatch among the layers, has not been adequately investigated. Here, we study the intralayer synchrony in multiplex networks, where the layers are different from one other, due to parameter mismatch in their local dynamics. In such a multiplex network, the intralayer coupling strength for the emergence of intralayer synchronization decreases upon the introduction of impurity among the layers, which is caused by a parameter mismatch in their local dynamics. Furthermore, the area of occurrence of intralayer synchronization also widens with increasing mismatch. We analytically derive a condition under which the intralayer synchronous solution exists, and we even sustain its stability. We also prove that, in spite of the mismatch among the layers, all the layers of the multiplex network synchronize simultaneously. Our results indicate that a multiplex network with mismatched layers can induce synchrony more easily than a multiplex network with identical layers. [ABSTRACT FROM AUTHOR]

We study the influence of the coexisting steady states in high-dimensional systems on the dynamical evolution of the vector field when a slow-varying periodic excitation is introduced. The model under consideration is a coupled system of Bonhöffer–van der Pol (BVP) equations with a slow-varying periodic excitation. We apply the modified slow–fast analysis method to perform a detailed study on all the equilibrium branches and their bifurcations of the generalized autonomous system. According to different dynamical behaviors, we explore the dynamical evolution of existing attractors, which reveals the coexistence of a quasi-periodic attractor with diverse types of bursting attractors. Further investigation shows that the coexisting steady states may cause spiking oscillations to behave in combination of a 2D torus and a limit cycle. We also identify a period-2 cycle bursting attractor as well as a quasi-periodic attractor according to the period-2 limit cycle. [ABSTRACT FROM AUTHOR]

Synchronization among uncoupled oscillators can emerge when common noise is applied on them and is famously known as noise-induced synchronization. In previous studies, it was assumed that common noise may drive all the oscillators at the same time when they are static in space. Understanding how to develop a mathematical model that apply common noise to only a fraction of oscillators is of significant importance for noise-induced synchronization. Here, we propose a direction-dependent noise field model for noise-induced synchronization of an ensemble of mobile oscillators/agents, and the effective noise on each moving agent is a function of its direction of motion. This enables the application of common noise if the agents are oriented in the same direction. We observe not only complete synchronization of all the oscillators but also clustered states as a function of the ensemble density beyond a critical value of noise intensity, which is a characteristic of the internal dynamics of the agents. Our results provide a deeper understanding on noise-induced synchronization even in mobile agents and how the mobility of agents affects the synchronization behaviors. [ABSTRACT FROM AUTHOR]

The article discusses a study which examined the contribution of mathematical models to the understanding of migraine because of their capability to dismantle fluctuations in the neuronal and autonomic subnetworks of the migraine cycle to present a biomarker of migraine in the migraine-generator network (MGN). It is mentioned that migraine is a dynamic disease with a complex network where trigger factors, early premonitory symptoms, transition and tipping points are interdependent events.

Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analysing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In recent years, the complex network as the frontier of complex system has received more and more attention. Peer-to-peer (P2P) networks with openness, anonymity, and dynamic nature are vulnerable and are easily attacked by peerswithmalicious behaviors. Building trusted relationships among peers in a large-scale distributed P2P systemis a fundamental and challenging research topic. Based on interpersonal relationships among peers of large-scale P2P networks, we present prevention and trust evaluation scheme, called IRTrust. The framework incorporates a strategy of identity authentication and a global trust of peers to improve the ability of resisting the malicious behaviors. It uses the quality of service (QoS), quality of recommendation (QoR), and comprehensive risk factor to evaluate the trustworthiness of a peer, which is applicable for large-scale unstructured P2P networks. The proposed IRTrust can defend against several kinds of malicious attacks, such as simple malicious attacks, collusive attacks, strategic attacks, and sybil attacks. Our simulation results show that the proposed scheme provides greater accuracy and stronger resistance compared with existing global trust schemes. The proposed scheme has potential application in secure P2P network coding. [ABSTRACT FROM AUTHOR]

This paper discusses the mean-square tracking consensus of heterogeneous multi-agent systems with additive noise and time delay both over fixed and switching topologies. To weaken the noises, consensus gain is introduced into the control protocol. By using graph theory, stochastic analysis, matrix theory and velocity decomposition approach, sufficient conditions as well as the upper bound of time delay for the mean-square tracking consensus are obtained. Several simulations are given to verify the potential correctness of the results. [ABSTRACT FROM AUTHOR]

We study the spreading of renewable power fluctuations through grids with Ohmic losses on the lines. By formulating a network-adapted linear response theory, we find that vulnerability patterns are linked to the left Laplacian eigenvectors of the overdamped eigenmodes. We show that for tree-like networks, fluctuations are amplified in the opposite direction of the power flow. This novel mechanism explains vulnerability patterns that were observed in previous numerical simulations of renewable microgrids. While exact mathematical derivations are only possible for tree-like networks with a homogeneous response, we show that the mechanisms discovered also explain vulnerability patterns in realistic heterogeneous meshed grids by studying the IEEE RTS-1996 test system. [ABSTRACT FROM AUTHOR]

The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types. [ABSTRACT FROM AUTHOR]

Abstract: We investigate bifurcations in neuronal networks with a hub structure. It is known that hubs play a leading role in characterizing the network dynamical behavior. However, the dynamics of hubs or star-coupled systems is not well understood. Here, we study rather subnetworks with a star-like configuration. This coupled system is an important motif in complex networks. Thus, our study is a basic step for understanding structure formation in large networks. We use the Morris–Lecar neuron with class I and class II excitabilities as a node. Homogeneous (coupling the same class neurons) and heterogeneous (coupling different class neurons) cases are considered for both excitatory and inhibitory coupling. For the homogeneous system class II neurons are suitable for achieving both complete and cluster synchronization in excitatory and inhibitory coupling, respectively. For the heterogeneous system with inhibitory coupling, the class I hub neuron has a wider parameter region of synchronous firings than the class II hub. Moreover, the class I hub neuron with the excitatory synapse gives rise to bifurcations of synchronized states and multi-stability (coexistence of a few different states) is observed. [Copyright &y& Elsevier]

Abstract: In the recent article “Stochastic analysis of recurrence plots with applications to the detection of deterministic signals” (Physica D 237 (2008) 619–629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process. Nevertheless, we also clearly assert that an uncritical application of RQA may lead to wrong conclusions. [Copyright &y& Elsevier]

Abstract: Anomalous phase synchronization in nonidentical interacting oscillators is manifest as the increase of frequency disorder prior to synchronization. We show that this effect can be enhanced when a time-delay is included in the coupling. In systems of limit-cycle and chaotic oscillators we find that the regions of phase disorder and phase synchronization can be interwoven in the parameter space such that as a function of coupling or time-delay the system shows transitions from phase ordering to disorder and back. [Copyright &y& Elsevier]

Abstract: The human electroencephalogram (EEG) is globally characterized by a power spectrum superimposed with certain peaks, whereby the “alpha peak” in a frequency range of 8–14Hz is the most prominent one for relaxed states of wakefulness. We present simulations of a minimal dynamical network model of leaky integrator neurons attached to the nodes of an evolving directed and weighted random graph (an Erdős–Rényi graph). We derive a model of the dendritic field potential (DFP) for the neurons leading to a simulated EEG that describes the global activity of the network. Depending on the network size, we find an oscillatory transition of the simulated EEG when the network reaches a critical connectivity. This transition, indicated by a suitably defined order parameter, is reflected by a sudden change of the network''s topology when super-cycles are formed from merging isolated loops. After the oscillatory transition, the power spectra of simulated EEG time series exhibit a continuum superimposed with certain peaks. [Copyright &y& Elsevier]

We investigate forced synchronization between electrically coupled Morris–Lecar neurons with class I and class II excitability through numerical bifurcation analysis. We find that class II neurons have wider parameter regions of forced synchronization. However, the bifurcation structure and patterns of spikes for class II are complicated; there exist period-doubling bifurcations, interesting two-periodic oscillations and irregular bursting spikes with high values of the coefficient of variation of the interspike interval. [ABSTRACT FROM AUTHOR]

An ensemble approach is presented for the reconstruction of a phase synchronization diagram from time series. As an example system, we analyze a forced Colpitts oscillator to show that synchronization diagram reconstructed by a single nonlinear model depends sensitively upon the model parameters, which should be estimated with a considerable amount of care. This dependence can be crucial for a precise recovery of the synchronization phenomena. To overcome this weakness, an ensemble approach is introduced. Two types of techniques, namely, (I) ensemble regression and (II) ensemble classification, are developed to show that they provide much more robust and reliable reconstruction of the synchronization diagram compared to the conventional single modeling approach. [ABSTRACT FROM AUTHOR]

Abstract: We study possible interrelations between the 300-year record of the yearly sunspot numbers and the solar inertial motion (SIM) using the recently developed technique of synchronization analysis. Phase synchronization of the sunspot cycle and the SIM is found and statistically confirmed in three epochs (1734–1790, 1855–1875 and 1907–1960) of the whole period 1700–2000. These results give quantitative support to the hypothesis that there is a weak interaction between the solar activity and the SIM. [Copyright &y& Elsevier]

Abstract: We study the noise activated dynamics of a model excitable system that consists of a subcritical Hopf oscillator with a time delayed nonlinear feedback. The coherence of the noise driven pulses of the system exhibits a novel double peaked structure as a function of the noise amplitude. The two peaks correspond to separate optimal noise levels for excitation of single spikes and multiple spikes (bursts) respectively. The relative magnitudes of these peaks are found to be a sensitive function of time delay. The physical significance of our results and its practical implications in various real life systems are discussed. [Copyright &y& Elsevier]

The number of patients suffering from cardiovascular diseases increases unproportionally high with the increase of the human population and aging, leading to very high expenses in the public health system. Therefore, the challenge of cardiovascular physics is to develop high-sophisticated methods which are able to, on the one hand, supplement and replace expensive medical devices and, on the other hand, improve the medical diagnostics with decreasing the patient’s risk. Cardiovascular physics–which interconnects medicine, physics, biology, engineering, and mathematics–is based on interdisciplinary collaboration of specialists from the above scientific fields and attempts to gain deeper insights into pathophysiology and treatment options. This paper summarizes advances in cardiovascular physics with emphasis on a workshop held in Bad Honnef, Germany, in May 2005. The meeting attracted an interdisciplinary audience and led to a number of papers covering the main research fields of cardiovascular physics, including data analysis, modeling, and medical application. The variety of problems addressed by this issue underlines the complexity of the cardiovascular system. It could be demonstrated in this Focus Issue, that data analyses and modeling methods from cardiovascular physics have the ability to lead to significant improvements in different medical fields. Consequently, this Focus Issue of Chaos is a status report that may invite all interested readers to join the community and find competent discussion and cooperation partners. [ABSTRACT FROM AUTHOR]

Abstract: Recurrence plot based methods are highly efficient and widely accepted tools for the investigation of time series or one-dimensional data. We present an extension of the recurrence plots and their quantifications in order to study recurrent structures in higher-dimensional spatial data. The capability of this extension is illustrated on prototypical 2D models. Next, the tested and proved approach is applied to assess the bone structure from CT images of human proximal tibia. We find that the spatial structures in trabecular bone become more recurrent during the bone loss in osteoporosis. [Copyright &y& Elsevier]

We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are synchronized more closely by the collective dynamics and constitute the dynamical core of the network. The numerical observation of this hierarchical synchronization is supported with an analysis based on a mean field approximation and the master stability function. [ABSTRACT FROM AUTHOR]

We investigate the influence of noise on synchronization between the spiking activities of neurons with external impulsive forces. We first analyze the dependence of the synchronized firing on the amplitude and the angular frequency of the impulsive force in the noise-free system. Three cases (regular spiking, traveling wave, and chaotic spiking) with low synchronized firing are chosen to study effects due to noise. In each case we find that small noise can be a promoter of synchronization phenomena in neural activities, by choosing an appropriate noise intensity acting on some of the neurons. [ABSTRACT FROM AUTHOR]

Abstract: Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the phase-space trajectory. This provides us a better understanding of the structures occurring in recurrence plots. The relationship between the time-scales and line structures are of practical importance in cross recurrence plots. Using this relationship within cross recurrence plots, the time-scales of differently sampled or time-transformed measurements can be adjusted. An application to geophysical measurements illustrates the capability of this method for the adjustment of time-scales in different measurements. [Copyright &y& Elsevier]

We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-sample test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series. [ABSTRACT FROM AUTHOR]