Dynamical hysteresis and spatial synchronization in coupled non-identical chaotic oscillators

We identify a novel phenomenon in distinct (namely non-identical) coupled chaotic systems, which we term dynamical hysteresis. This behavior, which appears to be universal, is defined in terms of the system dynamics (quantified for example through the Lyapunov exponents), and arises from the presence of at least two coexisting stable attractors over a finite range of coupling, with a change of stability outside this range. Further characterization via mutual synchronization indices reveals that one attractor corresponds to spatially synchronized oscillators, while the other corresponds to desynchronized oscillators. Dynamical hysteresis may thus help to understand critical aspects of the dynamical behavior of complex biological systems, e.g. seizures in the epileptic brain can be viewed as transitions between different dynamical phases caused by time dependence in the brain’s internal coupling.     

A subharmonic dynamical bifurcation during in vitro epileptiform activity

Epileptic seizures are considered to result from a sudden change in the synchronization of firing neurons in brain neural networks. We have used an in vitro model of status epilepticus (SE) to characterize dynamical regimes underlying the observed seizure-like activity. Time intervals between spikes or bursts were used as the variable to construct first-return interpeak or interburst interval plots, for studying neuronal population activity during the transition to seizure, as well as within seizures. Return maps constructed for a brief epoch before seizures were used for approximating the local system dynamics during that time window. Analysis of the first-return maps suggests that intermittency is a dynamical regime underlying the observed epileptic activity. This type of analysis may be useful for understanding the collective dynamics of neuronal populations in the normal and pathological brain.     

Dynamical analogy between epileptic seizures and seismogenic electromagnetic emissions by means of nonextensive statistical mechanics

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and neurodynamics can be analyzed within similar mathematical frameworks. Recently, authors have shown that a dynamical analogy supported by scale-free statistics exists between seizures and earthquakes, analyzing populations of different seizures and earthquakes, respectively. The purpose of this paper is to suggest a shift in emphasis from the large to the small scale: our analyses focus on a single epileptic seizure generation and the activation of a single fault (earthquake) and not on the statistics of sequences of different seizures and earthquakes. We apply the concepts of the nonextensive statistical physics to support the suggestion that a dynamical analogy exists between the two different extreme events, seizures and earthquakes. We also investigate the existence of such an analogy by means of scale-free statistics (the Gutenberg–Richter distribution of event sizes and the distribution of the waiting time until the next event). The performed analysis confirms the existence of a dynamic analogy between earthquakes and seizures, which moreover follow the dynamics of magnetic storms and solar flares.     

Dynamical systems and complex systems theory to study unsteady combustion

Reacting flow fields are often subject to unsteadiness due to flow, reaction, diffusion, and acoustics. Further, flames can also exhibit inherent unsteadiness caused by various intrinsic instabilities. Interaction between various unsteady processes across multiple scales often makes combustion dynamics complex. Characterizing such complex dynamics is essential to ensure the safe and reliable operation of high efficiency combustion systems. Tools from nonlinear dynamics and complex systems theory provide new perspectives to analyze and interpret the data from real systems. They could also provide new ways of monitoring and controlling combustion systems. We discuss recent advances in studying unsteady combustion dynamics using the tools from dynamical systems theory and complex systems theory. We cover a range of problems involving unsteady combustion such as thermoacoustic instability, flame blowout, fire propagation, reaction chemistry and flow flame interaction.     

基于Kendall改进的同步算法癫痫脑网络分析

提出了一种基于Kendall等级相关改进的同步算法IRC(inverse rank correlation).Kendall等级相关是非线性动力学分析的一般化算法,可有效地度量变量间的非线性相关性.复杂网络的研究已逐渐深入到社会科学的各个领域,脑网络的研究已经成为当今脑功能研究的热点.利用改进的IRC算法,基于脑电EEG(electroencephalogram)数据来构建大脑功能性网络.对构建的脑功能网络的度指标进行了分析,以调查癫痫脑功能网络是否异于正常人.结果显示:使用该改进的算法能够对癫痫和正常脑功能网络显著区分,且只需要记录很短的脑电数据.实验结果数据表明,该方法适用于区分癫痫和正常脑组织网络度指标,它可有助于进一步地加深对大脑的神经动力学行为的研究,并为临床诊断提供有效工具.     

Group Foundations of Quantum and Classical Dynamics : Towards a Globalization and Classification of Some of Their Structures

This paper is devoted to a constructiveand critical analysis of the structure of certain dynamical systems from a group manifold point of view recently developed. This approach is especially suitable for discussing the structure of the quantum theory, the classical limit, the Hamilton-Jacobi theory and other problems such as the definition and globalization of the Poincaré-Cartan form which appears in the variational approach to higher order dynamical systems. At the same time, i t opens a way for the classification of all hamiltonian and lagrangian systems associated with suitably defined dynamical groups. Both classical and quantum dynamics are discussed, and examples of all the different structures appearingin the theory are provided, including a treatment of constrained and generalized higher order dynamical systems.     

Use of recurrence analysis to measure the dynamical stability of a multi-species community model

Quantifying the effects of species richness and environmental disturbance on the stability of communities is a long-standing challenge in ecology. In this study, multivariate recurrence analysis was used to assess the dynamical stability of modelled ecological communities subject to random, correlated environmental noise. Based on an analysis of biomass time series for each species, we show that two measures computed from the joint recurrence matrix, the Kolmogorov entropy and percent determinism, capture aspects of community stability that are not detected using the coefficient of variation for the whole community. In particular, when population fluctuations are correlated in time, recurrence analysis is a superior method for detecting the stabilizing effect of species richness on a community. We conclude that recurrence analysis is an appropriate tool for the analysis of ecological data, and that it may be particularly useful for detecting the relative importance of exogenous and endogenous drivers on the dynamics of ecological communities.     

Single-trigger stochastic resonance

Summary We discuss a recently discovered mechanism for stochastic resonance which involves only a single reference state with excitable dynamics and deterministic reinjection. While calculations based on an analogy with the shot effect capture the broadest features, detailed comparisons with specific dynamical systems suggest the need for certain refinements of the theory. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

The Emergence of Temporal Structures in Dynamical Systems

Dynamical systems in classical, relativistic and quantum physics are ruled by laws with time reversibility. Complex dynamical systems with time-irreversibility are known from thermodynamics, biological evolution, growth of organisms, brain research, aging of people, and historical processes in social sciences. Complex systems are systems that compromise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous emergence of distinctive temporal, spatial or functional structures. But, emergence is no mystery. In a general meaning, the emergence of macroscopic features results from the nonlinear interactions of the elements in a complex system. Mathematically, the emergence of irreversible structures is modelled by phase transitions in non-equilibrium dynamics of complex systems. These methods have been modified even for chemical, biological, economic and societal applications (e.g., econophysics). Emergence of irreversible structures can also be simulated by computational systems. The question arises how the emergence of irreversible structures is compatible with the reversibility of fundamental physical laws. It is argued that, according to quantum cosmology, cosmic evolution leads from symmetry to complexity of irreversible structures by symmetry breaking and phase transitions. Thus, arrows of time and aging processes are not only subjective experiences or even contradictions to natural laws, but they can be explained by quantum cosmology and the nonlinear dynamics of complex systems. Human experiences and religious concepts of arrows of time are considered in a modern scientific framework. Platonic ideas of eternity are at least understandable with respect to mathematical invariance and symmetry of physical laws. Heraclit’s world of change and dynamics can be mapped onto our daily real-life experiences of arrows of time.     

Kernel-based regression of drift and diffusion coefficients of stochastic processes

To improve the estimation of drift and diffusion coefficients of stochastic processes in case of a limited amount of usable data due to e.g. non-stationarity of natural systems we suggest to use kernel-based instead of histogram-based regression. We propose a method for bandwidth selection and compare it to a widely used cross-validation method. Kernel-based regression reveals an enhanced ability to estimate drift and diffusion especially for a small amount of data. This allows one to improve resolvability of changes in complex dynamical systems as evidenced by an exemplary analysis of electroencephalographic data recorded from a human epileptic brain.     

Models for the modern power grid

This article reviews different kinds of models for the electric power grid that can be used to understand the modern power system, the smart grid. From the physical network to abstract energy markets, we identify in the literature different aspects that co-determine the spatio-temporal multilayer dynamics of power system. We start our review by showing how the generation, transmission and distribution characteristics of the traditional power grids are already subject to complex behaviour appearing as a result of the the interplay between dynamics of the nodes and topology, namely synchronisation and cascade effects. When dealing with smart grids, the system complexity increases even more: on top of the physical network of power lines and controllable sources of electricity, the modernisation brings information networks, renewable intermittent generation, market liberalisation, prosumers, among other aspects. In this case, we forecast a dynamical co-evolution of the smart grid and other kind of networked systems that cannot be understood isolated. This review compiles recent results that model electric power grids as complex systems, going beyond pure technological aspects. From this perspective, we then indicate possible ways to incorporate the diverse co-evolving systems into the smart grid model using, for example, network theory and multi-agent simulation.     

Spectral coarse graining and synchronization in oscillator networks

Coarse graining techniques offer a promising alternative to large-scale simulations of complex dynamical systems, as long as the coarse-grained system is truly representative of the initial one. Here, we investigate how the dynamical properties of oscillator networks are affected when some nodes are merged together to form a coarse-grained network. Moreover, we show that there exists a way of grouping nodes preserving as much as possible some crucial aspects of the network dynamics. This coarse graining approach provides a useful method to simplify complex oscillator networks, and more generally, networks whose dynamics involves a Laplacian matrix.     

A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks

The combination of network sciences, nonlinear dynamics and time series analysis provides novel insights and analogies between the different approaches to complex systems. By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov chains, we introduce a network measure for characterizing the dynamics on state-transition networks with special focus on differentiating between chaotic and cyclic modes. One important property of this Lyapunov measure consists of its non-monotonous dependence on the cylicity of the dynamics. Motivated by providing proper use cases for studying the new measure, we also lay out a method for mapping time series to state transition networks by phase space coarse graining. Using both discrete time and continuous time dynamical systems the Lyapunov measure extracted from the corresponding state-transition networks exhibits similar behavior to that of the Lyapunov exponent. In addition, it demonstrates a strong sensitivity to boundary crisis suggesting applicability in predicting the collapse of chaos.     

Hierarchical organization unveiled by functional connectivity in complex brain networks

How do diverse dynamical patterns arise from the topology of complex networks? We study synchronization dynamics in the cortical brain network of the cat, which displays a hierarchically clustered organization, by modeling each node (cortical area) with a subnetwork of interacting excitable neurons. We find that in the biologically plausible regime the dynamics exhibits a hierarchical modular organization, in particular, revealing functional clusters coinciding with the anatomical communities at different scales. Our results provide insights into the relationship between network topology and functional organization of complex brain networks.     

Editorial: Ecological complex systems

Main aim of this topical issue is to report recent advances in noisy nonequilibrium processes useful to describe the dynamics of ecological systems and to address the mechanisms of spatio-temporal pattern formation in ecology both from the experimental and theoretical points of view. This is in order to understand the dynamical behaviour of ecological complex systems through the interplay between nonlinearity, noise, random and periodic environmental interactions. Discovering the microscopic rules and the local interactions which lead to the emergence of specific global patterns or global dynamical behaviour and the noise’s role in the nonlinear dynamics is an important, key aspect to understand and then to model ecological complex systems.     

Cross-correlation markers in stochastic dynamics of complex systems

The neuromagnetic activity (magnetoencephalogram, MEG) from healthy human brain and from an epileptic patient against chromatic flickering stimuli has been earlier analyzed on the basis of a memory functions formalism (MFF). Information measures of memory as well as relaxation parameters revealed high individuality and unique features in the neuromagnetic brain responses of each subject. The current paper demonstrates new capabilities of MFF by studying cross-correlations between MEG signals obtained from multiple and distant brain regions. It is shown that the MEG signals of healthy subjects are characterized by well-defined effects of frequency synchronization and at the same time by the domination of low-frequency processes. On the contrary, the MEG of a patient is characterized by a sharp abnormality of frequency synchronization, and also by prevalence of high-frequency quasi-periodic processes. Modification of synchronization effects and dynamics of cross-correlations offer a promising method of detecting pathological abnormalities in brain responses.     

Oscillatory activity in excitable neural systems

The brain is a complex system and exhibits various subsystems on different spatial and temporal scales. These subsystems are recurrent networks of neurons or populations that interact with each other. The single neurons are microscopic objects and evolve on a different time scale than macroscopic neural populations. To understand the dynamics of the brain, however, it is necessary to understand the dynamics of the brain network both on the microscopic and the macroscopic level and the interaction between the levels. The presented work introduces one to the major properties of single neurons and their interactions. The physical aspects of some standard mathematical models are discussed in some detail. The work shows that both single neurons and neural populations are excitable in the sense that small differences in an initial short stimulation may yield very different dynamical behaviour of the system. To illustrate the power of the neural population model discussed, the work applies the model to explain experimental activity in the delayed feedback system in weakly electric fish and the electroencephalogram (EEG).     

Renormalization group and instantons in stochastic nonlinear dynamics

Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magneto-hydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications.     

高等植物外周捕光天线LHCⅡ中的超快光动力学过程

利用飞秒抽运探测技术及时间分辨荧光(TRPL)等光谱技术对高等植物LHCⅡ中的超快光动力学过程进行了研究。在其时间分辨荧光光谱中表现出了明显的各向异性特性。实验上观察了LHCⅡ中色素间的能量传递过程,由飞秒动力学发现,单体内Chlb到邻近的Chla之间的能量传递在200～300fs的时间尺度,Chla激子带间的能量弛豫发生在几百飞秒,不同单体Chla分子间能量分布过程在几个皮秒。而时间分辨荧光和飞秒动力学过程中上百皮秒的慢过程归属于不同聚集体间的能量平衡过程或分子构象变化。