Complex Natural Systems Research Articles

On Multiscaling of Parkinsonian Rest Tremor Signals and Their Classification.

Self-similar stochastic processes and broad probability distributions are ubiquitous in nature and in many man-made systems. The brain is a particularly interesting example of (natural) complex system where those features play a pivotal role. In fact, the controversial yet experimentally validated "criticality hypothesis" explaining the functioning of the brain implies the presence of scaling laws for correlations. Recently, we have analyzed a collection of rest tremor velocity signals recorded from patients affected by Parkinson's disease, with the aim of determining and hence exploiting the presence of scaling laws. Our results show that multiple scaling laws are required in order to describe the dynamics of such signals, stressing the complexity of the underlying generating mechanism. We successively extracted numeric features by using the multifractal detrended fluctuation analysis procedure. We found that such features can be effective for discriminating classes of signals recorded in different experimental conditions. Notably, we show that the use of medication (L-DOPA) can be recognized with high accuracy.

Methodical approaches to the formation of structural-parametric models of regulatory management of reproduction processes sustainability resistance in perennial agrocenoses

The necessity of forming structural-parametric models of normative management of the stability of reproductive processes in perennial agrocenoses is substantiated. Modern methods of managing the sustainability of reproductive processes in complex natural and man-made systems are considered: cognitive analysis and promising digital technologies. A structural model of the functional stability of reproductive processes in perennial agrocenoses has been developed, representing a hierarchical system that determines the structure of the relationships of functions and elements of reproductive processes, including the parameters of these relationships. An algorithm for the formation of a structural model of stability parameters has been developed, including the identification of functional areas of impacts; the formation of a system of evaluation indicators; the identification of functional ecological-economic and technological-economic relationships and the determination of their dimension; assessment of system-wide and functional stability of reproduction processes; determination of stability criteria and a system of restrictions; econometric modeling in order to determine the rational parameters of the stability of reproduction processes. The role of biotechnologies in ensuring the potential stability of agrocenoses, leveling the negative consequences as a result of climatic and chemical-man-made impacts on the elements of agrocenosis is substantiated. The tools of management of biotechnological processes in the elements of agrocenosis according to the criteria of adaptability, biologization and rational nature management are proposed. The normative-parametric model of ensuring the stability of reproductive processes has been developed, the main purpose of which is to substantiate the regulators (tools) of bringing the system to a stable state. The effectiveness of the adjustment of agrotechnological regulations in order to bring the indicators of the state of the agroecosystem to the normative level of stability is substantiated.

Al and H incorporation and Al-diffusion in natural rutile and its high-pressure polymorph TiO 2 (II)

Abstract Rutile is an important accessory mineral in metamorphic rocks and is used as a geothermobarometer or geochronometer. This study aims to bridge the gap between diffusion studies in simplified and complex natural systems by investigating the incorporation and mobility of Al in natural rutile and its high-pressure polymorph TiO 2 (II). Experiments were performed at 0.1 MPa to 7 GPa, 1223–1373 K, at buffered μ(Al 2 O 3 ) and with f O 2 constrained to ≤CCO, which is the equilibrium between graphite and a CO-CO 2 gas phase. Based on electron probe microanalysis, secondary ion mass spectrometry and Fourier transform infrared analyses, we suggest a complex combination of mechanisms to explain the incorporation of Al and H in natural rutile and TiO 2 (II). This includes: (1) the incorporation of Al 3+ on octahedral Ti-sites charge balanced by the formation of oxygen vacancies; and (2) the incorporation of oxygen in interstitial positions charge balanced by hydrogen interstitials. Determined Al-diffusivities in natural TiO 2 are approximately eight to nine orders of magnitude faster compared to previously published data. A possible explanation includes a significantly enhanced rate of ionic diffusion through the combined effect of hydrolytic weakening, enhanced Al-diffusion through extended defects and to a minor extent oxygen fugacity variations. Consequently, results of this study question that the inferred high closure temperatures for the Al-in-rutile geothermobarometer can be applied to all natural systems.

Fluid-mineral dynamics at the Rincón de la Vieja volcano—hydrothermal system (Costa Rica) inferred by the study of major, minor and rare earth elements in the hyperacid crater lake

Volcanic lakes are complex natural systems and their chemical composition is related to a myriad of processes. The chemical composition of major, minor, Rare Earth Elements (REE) and physico-chemical parameters at the hyperacid crater lake of Rincón de la Vieja volcano (Costa Rica) are here investigated during February 2013–August 2014. The study of the lake chemical composition allows to identify the main geochemical processes occurring in the lake and to track the changes in the volcanic activity, both important for active volcanoes monitoring. The total REE concentration (∑REE) dissolved in the crater lake varies from 2.7 to 3.6 mg kg−1 during the period of observation. REE in the water lake samples normalized to the average volcanic local rock (REEN-local rock) are depleted in light REE (LREE). On the contrary REEN-local rock in the solids precipitated (mainly gypsum/anhydrite), from lake water samples in laboratory at 22°C, are enriched in LREE. The low variability of (La/Pr)N-local rock and (LREE/HREE)N-local rock ratios (0.92–1.07 and 0.66–0.81, respectively) in crater lake waters is consistent with the low phreatic activity (less than 10 phreatic eruptions in 2 years) observed during the period of observation. This period of low activity precedes the unrest started in 2015, thus, it could be considered as a pre-unrest, characterized by infrequent phreatic eruptions. No clear changes in the REE chemistry are associated with the phreatic eruption occurred at mid-2013. The results obtained investigating water-rock interaction processes at the Rincón de la Vieja crater lake show that rock dissolution and mineral precipitation/dissolution are the main processes that control the variability of cations composition over time. In particular, precipitation and dissolution of gypsum and alunite are responsible for the variations of REE in the waters. Despite the low variations of (La/Pr)N-local rock and (LREE/HREE)N-local rock ratios, this study allows to suggest that REE can be used, together with major elements, as practical tracers of water-rock interaction processes and mineral precipitation/dissolution at active hyperacid crater lakes over time, also during periods of quiescence and low phreatic activity.

Modelling intermittent anomalous diffusion with switching fractional Brownian motion

The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due to which the motion changes along the trajectories. Such effects manifest themselves as spatiotemporal correlations. Despite the broad occurrence of heterogeneous complex systems in nature, their analysis is still quite poorly understood and tools to model them are largely missing. We contribute to tackling this problem by employing an integral representation of Mandelbrot’s fractional Brownian motion that is compliant with varying motion parameters while maintaining long memory. Two types of switching fractional Brownian motion are analysed, with transitions arising from a Markovian stochastic process and scale-free intermittent processes. We obtain simple formulas for classical statistics of the processes, namely the mean squared displacement and the power spectral density. Further, a method to identify switching fractional Brownian motion based on the distribution of displacements is described. A validation of the model is given for experimental measurements of the motion of quantum dots in the cytoplasm of live mammalian cells that were obtained by single-particle tracking.

New method for the transient simulation of natural gas pipeline networks based on the fracture-dimension-reduction algorithm

The transient simulation technology of natural gas pipeline networks plays an increasingly prominent role in the scheduling management of natural gas pipeline network system. The increasingly large and complex natural gas pipeline network requires more strictly on the calculation efficiency of transient simulation. To this end, this paper proposes a new method for the transient simulation of natural gas pipeline networks based on fracture-dimension-reduction algorithm. Firstly, a pipeline network model is abstracted into a station model, inter-station pipeline network model and connection node model. Secondly, the pressure at the connection node connecting the station and the inter-station pipeline network is used as the basic variable to solve the general solution of the flow rate at the connection node, reconstruct the simulation model of the inter-station pipeline network, and reduce the equation set dimension of the inter-station pipeline network model. Thirdly, the transient simulation model of the natural gas pipeline network system is constructed based on the reconstructed simulation model of the inter-station pipeline network. Finally, the calculation accuracy and efficiency of the proposed algorithm are compared and analyzed for the two working conditions of slow change of compressor speed and rapid shutdown of the compressor. And the following research results are obtained. First, the fracture-dimension-reduction algorithm has a high calculation accuracy, and the relative error of compressor outlet pressure and user pressure is less than 0.1%. Second, the calculation efficiency of the new fracture-dimension-reduction algorithm is high, and compared with the nonlinear equations solving method, the speed-up ratios under the two conditions are high up to 17.3 and 12.2 respectively. Third, the speed-up ratio of the fracture-dimension-reduction algorithm is linearly related to the equation set dimension of the transient simulation model of the pipeline network system. The larger the equation set dimension, the higher the speed-up ratio, which means the more complex the pipeline network model, the more remarkable the calculation speed-up effect. In conclusion, this new method improves the calculation speed while keeping the calculation accuracy, which is of great theoretical value and reference significance for improving the calculation efficiency of the transient simulation of complex natural gas pipeline network systems.

Synergetic paradigm of the global world

All sociological paradigms are based on the existing picture of the world, which determines them through cognitive models. Thus, the Darwinian evolutionism and dialectical materialism that developed in the last century were mainly based on four cognitive models: scholastic (nature and society as texts), mechanistic (nature and society as machines), statistical (nature and society as balances of average values) and systemic (nature and society as organisms). Contemporary sociological paradigms - of social facts, social behavior, social definitions and determinism - are also based on these cognitive models; however, today social processes go beyond these cognitive models, and there is a growing interest in an interdisciplinary approach called ‘synergetics’ (1). The synergetic approach uses such concepts as ‘order’, ‘chaos’, ‘nonlinearity’, ‘uncertainty’, ‘instability’, ‘dissipative structures’, ‘bifurcation’, ‘attractor’ and etc. Synergetics studies the general laws of self-organization, stability and destruction of ordered structures in complex systems of various nature; it is a theory of self-organization and development of open systems of any origin [6]. The synergetic style of scientific thinking presupposes a probabilistic vision of the world, which developed in the 19th century. Synergetics contributes to the formation of a new type of scientific thinking - post-non-classical, to the inclusion of humanistic and axiological parameters in scientific research and to the development of non-linear thinking, proving the inadequacy of the model of consistent and gradual cumulative development. The new sociological paradigm should accept the idea of synergetics about the interconnectedness of epistemology and ontology, i.e. the idea that the cognitive activity of the subject changes reality: the very choice of the object, conceptual scheme, methods and the use of the results obtained forms, changes and destroys the ontological basis; therefore, the researcher is responsible for the world that he creates and reforms.

Assessment of train running safety on railway bridges based on velocity-related indices under random near-fault ground motions

Random analysis has emerged as the dominant approach for analyzing train-bridge coupled (TBC) systems, replacing deterministic analysis. This shift is driven by considerations of system economy and randomness. However, the seismic train running safety assessment with multiple non-Gaussian distribution parameters faces the double dilemma of low computational efficiency and inaccuracy for TBC systems. In this study, an approach is applied by the combination of the new point estimate method and moment expansion approximation (NPEM-MEA) to address this problem. Furthermore, the application of this approach is illustrated by the random dynamic responses of a three-dimensional TBC system subjected to random near-fault ground motions. Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method, and comparative analysis confirms the accuracy and efficiency of the method. Additionally, the influences of random near-fault ground motions are discussed based on the random dynamic responses and train running safety indices in the TBC system. The simulation results underscore the necessity of simultaneously considering the randomness of multiple parameters in seismic train running safety assessment. This methodology holds potential for safety assessments involving non-Gaussian random processes in complex systems of a similar nature.

DEEP PROCESS-DATA MINING FOR BUILDING OF ANALYTICAL MODELS: 1. MEDIUM-TERM FORECAST OF SPRING FLOOD EXTREMES FOR MOUNTAIN RIVERS

A standard methodology of deep process-data mining for building high-performance process-driven (analytical) models of complex natural systems was proposed. The method- ology (called as system-analytical modeling) is based on a system-hierarchical approach and deep mining of large datasets providing both extraction of the information hidden in such datasets and quantitative characterization of real processes occurring in natural systems. With its help, deep process-data mining of data (1951–2020) on spring flood discharge peaks and troughs (with ice motion) on 34 mountain rivers of the Altai-Sayan mountain country was performed. An analytical hydrological model of high performance (Nash-Sutcliffe criterion NSE = 0.78) was developed for the annual medium-term forecasting of discharge peaks and troughs in April using the data on meteorological conditions of the recent autumn and current winter periods. Flood peaks depend on autumn-winter precipitation (which determines 29% of the peak variance), landscape structure of river basins (14%), and winter air temperatures (0.8%). Spring floods on mountain rivers often threaten the life of local population that makes the developed model topical.

Organoids as complex (bio)systems.

Organoids are three-dimensional structures derived from stem cells that mimic the organization and function of specific organs, making them valuable tools for studying complex systems in biology. This paper explores the application of complex systems theory to understand and characterize organoids as exemplars of intricate biological systems. By identifying and analyzing common design principles observed across diverse natural, technological, and social complex systems, we can gain insights into the underlying mechanisms governing organoid behavior and function. This review outlines general design principles found in complex systems and demonstrates how these principles manifest within organoids. By acknowledging organoids as representations of complex systems, we can illuminate our understanding of their normal physiological behavior and gain valuable insights into the alterations that can lead to disease. Therefore, incorporating complex systems theory into the study of organoids may foster novel perspectives in biology and pave the way for new avenues of research and therapeutic interventions to improve human health and wellbeing.

Comparison of Machine Learning Models to Predict Lake Area in an Arid Area

Machine learning (ML)-based models are popular for complex physical system simulation and prediction. Lake is the important indicator in arid and semi-arid areas, and to achieve the proper management of the water resources in a lake basin, it is crucial to estimate and predict the lake dynamics, based on hydro-meteorological variations and anthropogenic disturbances. This task is particularly challenging in arid and semi-arid regions, where water scarcity poses a significant threat to human life. In this study, a typical arid area of China was selected as the study area, and the performances of eight widely used ML models (i.e., Bayesian Ridge (BR), K-Nearest Neighbor (KNN), Gradient Boosting Decision Tree (GBDT), Extra Trees (ET), Random Forest (RF), Adaptive Boosting (AB), Bootstrap aggregating (Bagging), eXtreme Gradient Boosting (XGB)) were evaluated in predicting lake area. Monthly lake area was determined by meteorological (precipitation, air temperature, Standardised Precipitation Evapotranspiration Index (SPEI)) and anthropogenic factors (ETc, NDVI, LUCC). Lake area determined by Landsat satellite image classification for 2000–2020 was analysed side-by-side with the Standardised Precipitation Evapotranspiration Index (SPEI) on 9 and 12-month time scales. With the evaluation of six input variables and eight ML algorithms, it was found that the RF models performed best when using the SPEI-9 index, with R2 = 0.88, RMSE = 1.37, LCCC = 0.95, and PRD = 1331.4 for the test samples. Furthermore, the performance of the ML model constructed with the 9-month time scale SPEI (SPEI-9) as an input variable (MLSPEI-9) depended on seasonal variations, with the average relative errors of up to 0.62 in spring and a minimum of 0.12 in summer. Overall, this study provides valuable insights into the effectiveness of different ML models for predicting lake area by demonstrating that the right inputs can lead to a remarkable increase in performance of up to 13.89%. These findings have important implications for future research on lake area prediction in arid zones and demonstrate the power of ML models in advancing scientific understanding of complex natural systems.

Fuzzy modelling on the depletion of forest biomass and forest-dependent wildlife population

This paper presents a system of non-linear differential equations describing the depletion of forest biomass and forest-dependent wildlife population caused by human population and its associated activities. The model incorporates the imprecise nature of the parameters, which are treated as triangular fuzzy numbers to reflect the inherent uncertainty. We utilised α cut to transform these imprecise parameters into intervals. Subsequently, employing the principles of interval mathematics, we effectively converted the related differential equation into a pair of distinct differential equations. By leveraging the signed distance of the fuzzy numbers, we further simplified the equations, resulting in a single differential equation, which led to the formulation of a defuzzified model. The existence of equilibrium points with their stability behaviour is presented. Furthermore, the existence of trans-critical bifurcation is analysed. Through numerical simulations, we observe significant differences between the solutions of system in crisp and fuzzy environments. These findings highlight the importance of using fuzzy models to accurately represent the dynamics of complex natural systems. Consequently, we conclude that fuzzy models provide a trustworthy representation of the dynamics of complex natural systems.

Prediction of soil moisture using BiGRU-LSTM model with STL decomposition in Qinghai-Tibet Plateau.

Ali Network data based on the Qinghai-Tibetan Plateau (QTP) can provide representative coverage of the climate and surface hydrometeorological conditions in the cold and arid region of the QTP. Among them, the plateau soil moisture can effectively quantify the uncertainty of coarse resolution satellite and soil moisture models. With the objective of constructing an "end-to-end" soil moisture prediction model for the Tibetan Plateau, a combined prediction model based on time series decomposition and a deep neural network is proposed in this article. The model first performs data preprocessing and seasonal-trend decomposition using loess (STL) to obtain the trend component, seasonal component and random residual component of the original time series in an additive way. Subsequently, the bidirectional gated recurrent unit (BiGRU) is used for the trend component, and the long short-term memory (LSTM) is used for the seasonal and residual components to extract the time series information. The experiments based on the measured data demonstrate that the use of STL decomposition and the combination model can effectively extract the information in soil moisture series using its concise and clear structure. The proposed model in this article has a stable performance improvement of 5-30% over a single model and existing prediction models in different prediction time domains. In long-range prediction, the proposed model also achieves the best accuracy in the shape and temporal domains described by using dynamic time warping (DTW) index and temporal distortion index (TDI). In addition, the generalization performance experiments show that the combined method proposed in this article has strong reference value for time series prediction of natural complex systems.

Non-additive entropies and statistical mechanics at the edge of chaos: a bridge between natural and social sciences.

The Boltzmann-Gibbs (BG) statistical mechanics constitutes one of the pillars of contemporary theoretical physics. It is constructed upon the other pillars-classical, quantum, relativistic mechanics and Maxwell equations for electromagnetism-and its foundations are grounded on the optimization of the BG (additive) entropic functional [Formula: see text]. Its use in the realm of classical mechanics is legitimate for vast classes of nonlinear dynamical systems under the assumption that the maximal Lyapunov exponent is positive (currently referred to as strong chaos), and its validity has been experimentally verified in countless situations. It fails however when the maximal Lyapunov exponent vanishes (referred to as weak chaos), which is virtually always the case with complex natural, artificial and social systems. To overcome this type of weakness of the BG theory, a generalization was proposed in 1988 grounded on the non-additive entropic functional [Formula: see text]. The index [Formula: see text] and related ones are to be calculated, whenever mathematically tractable, from first principles and reflect the specific class of weak chaos. We review here the basics of this generalization and illustrate its validity with selected examples aiming to bridge natural and social sciences. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)'.

A DAPSI(W)R(M) framework approach to characterization of environmental issues in touristic coastal systems. An example from Southern Spain

Coasts are complex natural and human systems subject to change via natural processes and human activity. Assimilation of this diverse set of drivers and responses and the relationships between them is a challenge in coastal management. We investigate the utility of the DAPSI(W)R(M) framework to identify indicators of environmental issues and the relations between human activities and the environment through a practical application on a coast with high levels of tourism-related activities. Components and indicators were assessed by a review of literature and existing data in the Málaga Province of southern Spain, focusing on coastal erosion and its relationship to the natural environment and social systems. The results indicate the utility of the DAPSI(W)R(M) framework to characterize key environmental issues that affect coastal areas, and provide an holistic vision of human activities and environmental processes. The application of this approach can improve coastal management through the development of a simple model that characterizes environmental issues from the causes to the consequences by means of indicators and the relationships between them. The cyclic form of the model permits an easy identification of where problems occur and who is involved with their resolution, helping with stakeholder mapping and decision-making regarding appropriate responses that can be taken to other administrative levels or other heavily developed tourist coastal areas.

Consciousness as an intelligent complex adaptive system: A neuroanthropological perspective

AbstractIn complexity theory, both the brain and consciousness are understood as trophic systems—they consume metabolic energy when they function. Complex systems are dynamic and nonlinear and comprise diverse entities that are interdependent and interconnected in such a way that information is shared and that entities adapt to one another. Some natural complex systems are complex adaptive systems (CAS), which are sensitive to change in relation to their environments and are often chaotic. Consciousness and the neural systems mediating consciousness may be modeled as CAS and, more specifically, as intelligent complex adaptive systems (ICAS), where intelligence means that a nervous system can solve problems successfully by intervening between sensory input and behavioral output. Evolution of any ICAS will result in emergent properties, particularly advanced brains. Two processes are involved in integrating experience and knowledge: the effort after meaning and the effort after truth. These efforts are mediated by the predominance given to direct experience presented to the brain's sensorium and modeling processes mediated by higher cognitive functions. Understanding consciousness as an ICAS has profound repercussions in how anthropology conceives of culture.

Clustering of Multilayer Networks Using Joint Learning Algorithm With Orthogonality and Specificity of Features.

Complex systems in nature and society consist of various types of interactions, where each type of interaction belongs to a layer, resulting in the so-called multilayer networks. Identifying specific modules for each layer is of great significance for revealing the structure-function relations in multilayer networks. However, the available approaches are criticized undesirable because they fail to explicitly the specificity of modules, and balance the specificity and connectivity of modules. To overcome these drawbacks, we propose an accurate and flexible algorithm by joint learning matrix factorization and sparse representation (jMFSR) for specific modules in multilayer networks, where matrix factorization extracts features of vertices and sparse representation discovers specific modules. To exploit the discriminative latent features of vertices in multilayer networks, jMFSR incorporates linear discriminant analysis (LDA) into non-negative matrix factorization (NMF) to learn features of vertices that distinguish the categories. To explicitly measure the specificity of features, jMFSR decomposes features of vertices into common and specific parts, thereby enhancing the quality of features. Then, jMFSR jointly learns feature extraction, common-specific feature factorization, and clustering of multilayer networks. The experiments on 11 datasets indicate that jMFSR significantly outperforms state-of-the-art baselines in terms of various measurements.

Neural tissue-engineered prevascularization in vivo enhances peripheral neuroregeneration via rapid vascular inosculation.

Neural tissue engineering techniques typically face a significant challenge, simulating complex natural vascular systems that hinder the clinical application of tissue-engineered nerve grafts (TENGs). Here, we report a subcutaneously pre-vascularized TENG consisting of a vascular endothelial growth factor-induced host vascular network, chitosan nerve conduit, and inserted silk fibroin fibers. Contrast agent perfusion, tissue clearing, microCT scan, and blood vessel 3D reconstruction were carried out continuously to prove whether the regenerated blood vessels were functional. Moreover, histological and electrophysiological evaluations were also applied to investigate the efficacy of repairing peripheral nerve defects with pre-vascularized TENG. Rapid vascular inosculation of TENG pre-vascularized blood vessels with the host vascular system was observed at 4​d bridging the 10​mm sciatic nerve defect in rats. Transplantation of pre-vascularized TENG in vivo suppressed proliferation of vascular endothelial cells (VECs) while promoting their migration within 14​d post bridging surgery. More importantly, the early vascularization of TENG drives axonal regrowth by facilitating bidirectional migration of Schwann cells (SCs) and the bands of Büngner formation. This pre-vascularized TENG increased remyelination, promoted recovery of electrophysiological function, and prevented atrophy of the target muscles when observed 12 weeks post neural transplantation. The neural tissue-engineered pre-vascularization technique provides a potential approach to discover an individualized TENG and explore the innovative neural regenerative process.

Rapid and selective removal of aristolochic acid I in natural products by vinylene-linked iCOF resins

Rapid, efficient, and selective removal of toxicants such as aristolochic acid I (AAI) from complex natural product systems is of great significance for the safe use of herbal medicines or medicine-food plants. Addressing this challenge, we develop a high-performance separation approach based on ionic covalent organic frameworks (iCOFs) to separate and remove AAI. Two vinylene-linked iCOFs (NKCOF-46-Br- and NKCOF-55-Br-) with high crystallinity are fabricated in a green and scalable fashion via a melt polymerization synthesis method. The resulting materials exhibit a uniform morphology, high stability, fast equilibrium time, and superior affinity and selectivity for AAI. Compared to conventional separation media, NKCOF-46-Br- and NKCOF-55-Br- achieve the record high adsorption capacities of 246.0 mg g−1 and 178.4 mg g−1, respectively. Various investigations reveal that the positively charged framework and favorable pore microenvironment of iCOFs contribute to their high selectivity and adsorption efficiency. Moreover, the iCOFs exhibit excellent biocompatibility by in vivo toxicity assays. This study paves a new avenue for the rapid, selective and efficient removal of toxicants from complex natural systems.

Entropy evolution at generic power-law edge of chaos

For strongly chaotic classical systems, a basic statistical–mechanical connection is provided by the averaged Pesin-like identity (the production rate of the Boltzmann–Gibbs entropy SBG=−∑i=1Wpilnpi equals the sum of the positive Lyapunov exponents). In contrast, at a generic edge of chaos (vanishing maximal Lyapunov exponent) we have a subexponential divergence with time of initially close orbits. This typically occurs in complex natural, artificial and social systems and, for a wide class of them, the appropriate entropy is the nonadditive one Sqe=1−∑i=1Wpiqeqe−1(S1=SBG) with qe≤1. For such weakly chaotic systems, power-law divergences emerge involving a set of microscopic indices {qk}’s and the associated generalized Lyapunov coefficients. We establish the connection between these quantities and (qe,Kqe), where Kqe is the Sqe entropy production rate.