Complex Dynamical Systems Research Articles

Dynamical Complexity in Geomagnetically Induced Current Activity Indices Using Block Entropy

Geomagnetically Induced Currents (GICs) are a manifestation of space weather events at ground level. GICs have the potential to cause power failures in electric grids. The GIC index is a proxy of the ground geoelectric field derived solely from geomagnetic field data. Information theory can be used to shed light on the dynamics of complex systems, such as the coupled solar wind–magnetosphere–ionosphere–ground system. We performed block entropy analysis of the GIC activity indices at middle-latitude European observatories around the St. Patrick’s Day March 2015 intense magnetic storm and Mother’s Day (or Gannon) May 2024 superintense storm. We found that the GIC index values were generally higher for the May 2024 storm, indicating elevated risk levels. Furthermore, the entropy values of the SYM-H and GIC indices were higher in the time interval before the storms than during the storms, indicating transition from a system with lower organization to one with higher organization. These findings, including the temporal dynamics of the entropy and GIC indices, highlight the potential of this method to reveal pre-storm susceptibility and relaxation processes. This study not only adds to the knowledge of geomagnetic disturbances but also provides valuable practical implications for space weather forecasting and geospatial risk assessment.

ML-MCTDH-Aid: An auxiliary package for multilayer multiconfiguration time-dependent Hartree calculations.

The multilayer-multiconfiguration time-dependent Hartree (ML-MCTDH) method has garnered significant attention in the realm of theoretical chemistry owing to its powerful ability to perform numerically exact descriptions of multi-dimensional quantum dynamics and exhibit the remarkable performance in simulating the nonadiabatic dynamics of complex systems. Despite the availability of computational packages within the ML-MCTDH framework, executing these calculations seamlessly is not a straightforward task. Typically, substantial efforts are necessitated to configure the correct inputs for ML-MCTDH calculations, which require to correctly define several non-trivial parameters, to reasonably setup the optimal tree expansion of wavefunctions, and to properly select basis function numbers. To address these challenges, we have developed an auxiliary package named ML-MCTDH-Aid, which facilitates the setup of ML-MCTDH calculations using the Heidelberg MCTDH package in a user-friendly manner. This package is primarily tailored to handle the high-dimensional nonadiabatic dynamics governed by the Hamiltonian composed of several electronic states, several vibrational modes and their linear vibronic coupling terms. It automatically generates multiple essential input files, and all the calculations can be performed in an all-in-one black-box easy-to-use manner. To show the utility of the ML-MCTDH-Aid package, we provide a step-by-step tutorial that demonstrates running ML-MCTDH studies on three models. These examples illuminate how the utilization of the ML-MCTDH-Aid package significantly enhances the efficiency and effectiveness of ML-MCTDH calculations. This substantially boosts the accessibility of ML-MCTDH calculations in tackling the high-dimensional quantum dynamics of complex systems.

From a latent variable to a complex dynamic system conceptualization of the therapeutic alliance.

From a latent variable to a complex dynamic system conceptualization of the therapeutic alliance.

System Dynamics-Based Integrated Benefit Analysis of Low-Carbon Management Process of Municipal Solid Waste

With rapid economic development, the amount of the municipal solid waste (MSW) generated has increased dramatically. To improve the socio-economic benefits and environmental impacts of the low-carbon management of MSW, it is crucial to identify the drivers of Greenhouse Gas (GHG) emissions from MSW treatment and assess their systematic and comprehensive benefits. The factor decomposition method is one of the most commonly used methods focused on identifying GHG emission-influencing factors, while the system dynamics (SD) method is commonly used to analyze the causal relationships between linear and nonlinear variables in complex dynamic systems. Unlike existing studies that account for and evaluate MSW from a static perspective, this paper innovatively combines the LMDI-SD model to identify and quantify the GHG emission drivers of MSW and evaluate the benefits of decarbonizing the MSW management in China from a comprehensive and systematic perspective. The results show that the dominant factor driving MSW GHG emissions from 2010 to 2022 is the economic development factor, ∆EED, while the intensity of MSW generation ∆EGI and the structure of MSW treatment ∆ETS play a stronger inhibiting role. Based on this, the SD model is constructed to simulate different scenarios, and the analysis shows that increasing the waste separation rate (S3) is the most effective measure to improve the socio-economic benefits and environmental impacts of the system. Compared with the base scenario, the socio-economic benefits and environmental impacts in 2050, for example, are increased by 82.8% and 43.4%, respectively. Improving the utilization rate of landfill gas (S1), reducing the per capita amount of MSW generated (S4) and increasing the incineration rate of MSW (S2) also have significant advantages for the improvement of benefits. Finally, some policy recommendations for the improvement of the comprehensive benefits of low-carbon MSW management systems are proposed to help policymakers make appropriate decisions.

Machine learning emulators of dynamical systems for understanding ecosystem behaviour

Minimal models (MM) aim to capture the simplified behaviour of complex systems to facilitate system-level analyses that would be unfeasible with more sophisticated numerical models. However, the choices involved in minimal model development heavily rely on expert knowledge, a source of bias that can interfere with good modelling practices. In this paper, a new method is proposed in which a machine learning (ML) model is trained with transient data generated by a detailed physically-based numerical model, predicting the rate of change of the target state variables given their current value and additional drivers. The trained model is then used to mimic the analysis made with traditional minimal models. This approach (ML-MM) is deployed in a semiarid hillslope ecosystem characterising its soil and vegetation components. The ML-MM outputs share most of the general features with previous expert-based results but show a better ability of the hillslope to (1) recover its vegetation, (2) resist total disappearance of the soil and (3) reach substantially higher soil depths in steady state. Furthermore, a new intermediate stable equilibrium is found between the already known healthy and degraded ones, revealing a more complex pattern of ecosystem collapse that avoids a critical shift, as supported by numerical model simulations. The transient behaviour is also investigated, from which we conclude that the system can exhibit strong reactivity, that is, an initial deviation away from equilibrium after a perturbation. In conclusion, the present study demonstrates the potential of ML-MM to obtain new scientific insights on complex systems that might be missed by expert-based alternatives. Hence, minimal models may benefit greatly from incorporating detailed numerical models and data-driven simplification in their development process. Ultimately, this methodology could be applicable to many fields of study and even be expanded to observational data, enhancing our understanding of real-world complex system dynamics.

Mathematical simulation modeling of an automated system to reduce heat stress and convergence to theoretical values

Relevance. It is known that the productive qualities of animals depend on the genetic component and animal housing conditions. Due to the fact that the microclimate of the room should be perceived as a complex dynamic system, it is necessary to determine a number of factors that have the greatest influence on its relationship with living organisms. In order to create favorable conditions in the premises for keeping cattle, it is necessary to comply with the regulated values from normative documents. The biggest problem at the moment in microclimate regulation is the detrimental effect of heat stress. As a rule, it is caused by uncontrolled temperature increase in the cattle housing. To date, heat stress is combated in several ways: the use of specialized equipment, pharmacological, prevention of harmful effects, genetic. At the same time used methods to reduce the impact of heat stress is still insufficient, in view of which nowadays research is conducted to create new systems.The purpose of the study was to conduct simulation modeling to verify the values obtained from theoretical studies. Computer-aided design and data processing programs such as Compass-3D and Microsoft Office were used.Results. The results of the study allow us to establish that the velocity of the outgoing air flow at the moment of exit from the duct is 1.615 m/s, and the velocity of the air flow when approaching the cattle decreases and reaches 0.450 m/s. These values are lower than the theoretical one by 15% and 10% respectively. The relationship between the results of simulation modeling and theoretical values is direct and has a strong closeness of relationship, convergence is equal to 0.86.

Unlocking Interpretable Prediction of Battery Random Discharge Capacity With Domain Adaptative Physics Constraint

AbstractTracking the battery discharge capacity is significant, yet challenging due to complicated degradation patterns as well as varying or even random usage scenarios. This work proposes a physics‐constrained domain adaptation framework to predict the capacities during random discharge with non‐destructive mechanism diagnosis using early or random discharging information. By imposing the impedance as physical constraints in a domain adaptative layer, the interpretability and generalization of the model can be improved as the physics‐constrained layer provides physical insights into the battery mechanism characteristics, enabling onboard and non‐destructive diagnosis without complex tests. The learned impedances in the physics‐constrained layer are well‐fitted to the real ones, suggesting accurate physical insights and, therefore, good interpretability of the trained model. Furthermore, apart from capacity prediction, the aging mechanisms of the cell can be interpreted through the learned physics from this deep learning framework without impedance measurement. Such interpretation has also been validated experimentally through post‐mortem analysis. This work provides an example of grey‐box modeling of complex dynamic systems where deep learning models can provide certain physical details to increase the model's interpretability.

Supplemental Material for From a Latent Variable to a Complex Dynamic System Conceptualization of the Therapeutic Alliance

Supplemental Material for From a Latent Variable to a Complex Dynamic System Conceptualization of the Therapeutic Alliance

Reconstructing professional identity through collaboration in pluralistic approaches

ABSTRACT This study investigates the reconstruction of professional identity among three experienced language teacher educators through collaboration in pluralistic approaches. Framing identity within a narrative-based understanding and exploring the interactional aspects of collaboration through the Complex Dynamic Systems Theory (CDST) lens, the study moves beyond traditional narrative inquiries in teacher education. Employing an autobiographical narrative approach, the study metaphorically represents professional identity reconstruction as complex dynamic systems. Grounded in autobiographical accounts from a year-long international collaboration on developing teacher competencies for pluralistic approaches, the study identifies emerging themes such as the role of peer collaboration, digital tools, and contextual influences in identity transformation. Findings suggest implications for professional development through collaborative and international networks in language education. The study contributes to understanding language educator identity as a dynamic, ongoing interpretive process in collaborative settings, offering insights for teacher education.

Teachers’ collaborative knowledge building in professional learning communities: connecting interaction patterns to learning gains

Teacher professional learning communities (PLCs) have the potential to result in teacher professional development, provided that effective communication takes place during PLC meetings. Building on the perspective of collaborative knowledge building, this study examined teachers’ interaction patterns during these meetings. Connections were explored between teachers’ self-perceived learning gains from a PLC and the interaction patterns that occurred. From a larger set of PLCs in the Netherlands, four cases were selected that differed regarding teachers’ learning gains profiles. Orbital decomposition analysis, a technique used to study emerging patterns in complex dynamic systems, was used to examine the extent to which interaction patterns were characterized by conversational moves associated with knowledge building. Results from these analyses showed that in general, all PLCs showed relatively few knowledge-building patterns. However, the low-gains PLC was a bit more focused on exchanging information and opinions. High-gains PLCs’ interactions were characterized more by open and involved communication. Conversation in mixed-gains PLCs revealed a connection between teachers’ knowledge gains and question–answer patterns, and between teachers’ changes in beliefs and elaborating upon opinions. Together, these results point to qualitative differences in the interactions of teacher PLCs who experience higher versus lower learning gains. Implications for the role of the facilitator are discussed.

Systemic wisdom and complex strategic competition: a systems approach

Strategic competition is a reoccurring phrase in the foreign policy and national security community to describe the current relationship between the United States and China. However, strategic competition and the goals of such a competition are rarely defined. A clear definition of strategic competition is necessary to grasp its implications for the United States and the world. This is even more important as the strategic competition between the United States and China is complex. Applying complexity and systems theory to strategic competition, it is framed as an interaction between two complex systems in a complex international system. By drawing on the competencies of systemic wisdom, policymakers concerned with strategic competition can have a toolkit for better understanding the complexity of strategic competition. While complexity cannot be controlled nor put aside, working with the complex system dynamics of strategic competition can help the United States manage and succeed in strategic competition.

Discrete adaptive sliding mode control for uncertain fractional-order Hammerstein system

This study explores controlling discrete fractional-order Hammerstein systems through two different approaches. The first method involves a detailed exploration of discrete sliding mode control (SMC), while the second method employs adaptive sliding mode techniques to address challenges posed by unknown time-varying system parameters. The aim is to enhance control strategies for these systems by ensuring stability and robustness amid evolving parameters. Stability analysis using Lyapunov Theory is carried out to establish the stability of the proposed control schemes. Comprehensive reachability analysis is then performed to show that the system reaches a quasi-sliding mode in finite time. The effectiveness of the proposed methods is thoroughly evaluated using simulation cases, covering three distinct scenarios. Finally, a discussion section analyzes the simulation outcomes and assesses the efficiency methodologies in handling complex system dynamics. Through comparative analysis and discussion, this study contributes to advancing control strategies tailored for systems characterized by fractional-order dynamics and varying parameters.

Perception Development of L2 English and L3 Polish Coda Obstruent by L1 German Adult Multilinguals

Research into L3 phonological acquisition has grown in the past decade, yet perceptual studies remain scarce. Existing studies report complex interactions between the phonetic categories of multilinguals’ L1, L2 and L3, depending on investigated feature and stage of L3 learning. This small-scale study, grounded in Complex Dynamic Systems Theory, examines the development of coda obstruent perception in seven beginner learners of Polish as an L3 (aged 21–39), with German as their L1 and English as their L2. Over ten months of instructed L3 learning, participants were tested four times using a timed forced-choice goodness task in both L2 and L3. Additionally, three participants provided monthly data between the second and fourth testing. Analyses across the sample revealed a competitive relationship between L2 and L3 perception, with L2 accuracy declining as L3 accuracy improved. Individual data, however, indicated more varied patterns: while one learner followed the overall trend, another exhibited decreasing accuracy in both their L2 and L3, and the third maintained accurate L2 perception alongside more accurate yet increasingly variable L3 perception. These findings highlight the value of analyzing both overall trends and individual data to better understand multilingual speech perception development, and suggest that, with growing L3 experience, the newly learnt L3 may influence L2 perception of a phonological process shared in the L1 and marked in the L2.

Forecast modeling of the dynamics of main resources and construction of a simulation system for managing the activities of the regional energy system of the Samara region

Regional energy systems are complex dynamic systems that operate in conditions of constant changes in the external environment. In this regard, the task of developing complex management decisions and conducting a systemic analysis of the efficiency of its activities arises. To solve this problem, it is necessary to improve the mathematical models of the dynamics of capital, labor and fuel resources, since they have the greatest impact on the energy output of the energy system. The paper analyzes existing methods of mathematical description of the dynamics of basic resources and their shortcomings. The paper considers covariance-stationary models of time series in the form of difference equations with a deterministic polynomial trend. The paper presents the results of mathematical modeling of the dynamics of capital, labor and fuel resources based on statistical data on the activities of the energy system of the Samara Region, published in the annual reports of regional ministries and energy companies, and conducts a statistical analysis of them. Based on a comparative analysis of mathematical models, the most effective models of the dynamics of capital, labor and fuel resources with the best predictive qualities were selected. Also, in the work, a single-loop simulation model of the energy system management system was constructed by forming investments for the renewal of capital resources and the structure of the decision support system (DSS) was developed, allowing the formation of mathematically sound management decisions.

Analysis of the spiking dynamics of a diode laser with dual optical feedback

In a complex dynamical system, noise, feedback, and external forces shape behavior that can range from regularity to high-dimensional chaos. Multiple feedback sources can significantly alter its dynamics, potentially even suppressing the system’s output. This study investigates the impact of competing feedback sources on a stochastic complex dynamical system using a photonic neuron—a diode laser with external optical feedback. By varying the feedback intensities from two external reflectors, we explore how dual feedback influences the system’s behavior. Using ordinal analysis and advanced measures of complexity, we quantify the system’s dynamics and uncover underlying symmetries. Our findings reveal that the interaction between the two feedback sources induces a more intense deterministic behavior, distinct from the dynamics produced by each feedback source individually. Additionally, clear temporal symmetries emerge across all dynamical regimes. By employing a novel entropy-vector representation, we are able to identify a unique signature that characterizes the system’s dynamics.

A machine learning approach to predicting dynamical observables from network structure

Estimating the outcome of a given dynamical process from structural features is a key unsolved challenge in network science. This goal is hampered by difficulties associated with nonlinearities, correlations and feedbacks between the structure and dynamics of complex systems. In this work, we develop an approach based on machine learning algorithms that provides an important step towards understanding the relationship between the structure and dynamics of networks. In particular, it allows us to estimate from the network structure the outbreak size of a disease starting from a single node, as well as the degree of synchronicity of a system made up of Kuramoto oscillators. We show which topological features of the network are key for this estimation and provide a ranking of the importance of network metrics with much higher accuracy than previously done. For epidemic propagation, the k-core plays a fundamental role, while for synchronization, the betweenness centrality and accessibility are the measures most related to the state of an oscillator. For all the networks, we find that random forests can predict the outbreak size or synchronization state with high accuracy, indicating that the network structure plays a fundamental role in the spreading process. Our approach is general and can be applied to almost any dynamic process running on complex networks. Also, our work is an important step towards applying machine learning methods to unravel dynamical patterns that emerge in complex networked systems.

Analysis of the internal motions of thermoresponsive polymers and single chain nanoparticles.

Data-driven techniques, such as proper orthogonal decomposition (POD) and uniform manifold approximation & projection (UMAP), are powerful methods for understanding polymer behavior in complex systems that extend beyond ideal conditions. They are based on the principle that low-dimensional behaviors are often embedded within the structure and dynamics of complex systems. Here, the internal motions of a thermoresponsive, LCST polymer are investigated for two cases: (1) the coil-to-globule transition that occurs as the system is heated above its critical temperature and (2) intramolecularly crosslinked, single chain nanoparticles (SCNPs) both above and below the critical temperature (TC). Our results demonstrate that POD can successfully extract the key features of the dynamics for both polymer globules and SCNPs. In the globular state, our results show that the relaxation modes are distorted relative to the coil state and relaxation times decrease upon chain collapse. After randomly crosslinking a globule to produce a SCNP, we observe a further distortion of the relaxation modes that depends strongly upon the particular set of monomers that are crosslinked. Yet, different sets of crosslinked monomers produce similar relaxation times for the SCNP. We observe that for SCNPs below the critical temperature, the relaxation times decrease with increasing crosslink density while above the critical temperature, they increase as crosslink density increases. Finally, using UMAP we categorize the local structure of SCNPs and examine the influence of the local structure on SCNP relaxation dynamics.

The role of Micro-biome engineering in enhancing Food safety and quality.

Microbiome engineering has emerged as a transformative approach to enhancing food safety and quality by strategically modulating microbial communities. This review critically examines state-of-the-art techniques, including synthetic biology, artificial intelligence (AI), and systems biology, that are revolutionizing our ability to improve nutritional profiles, extend shelf life, and optimize food production processes. The review further explores complex social, ethical, and regulatory considerations, emphasizing the importance of robust public engagement and the establishment of standardized frameworks to ensure safe and effective implementation. While microbiome engineering holds significant promise for revolutionizing food safety and quality control, further research is needed to address critical challenges, including understanding microbial dynamics in complex food systems and developing harmonized regulatory frameworks. By bridging interdisciplinary gaps, this paper underscores the necessity of collaborative efforts to unlock the full potential of microbiome-driven innovations for a more resilient and sustainable food industry.

Filling data analysis gaps in time-resolved crystallography by machine learning.

There is a growing understanding of the structural dynamics of biological molecules fueled by x-ray crystallography experiments. Time-resolved serial femtosecond crystallography (TR-SFX) with x-ray Free Electron Lasers allows the measurement of ultrafast structural changes in proteins. Nevertheless, this technique comes with some limitations. One major challenge is the quality of data from TR-SFX measurements, which often faces issues like data sparsity, partial recording of Bragg reflections, timing errors, and pixel noise. To overcome these difficulties, conventionally, large volumes of data are collected and grouped into a few temporal bins. The data in each bin are then averaged and paired with the mean of their corresponding jittered timestamps. This procedure provides one structure per bin, resulting in a limited number of averaged structures for the entire time interval spanned by the experiment. Therefore, the information on ultrafast structural dynamics at high temporal resolution is lost. This has initiated research for advanced methods of analyzing experimental TR-SFX data beyond the standard binning and averaging method. To address this problem, we use a machine learning algorithm called Nonlinear Laplacian Spectral Analysis (NLSA), which has emerged as a promising technique for studying the dynamics of complex systems. In this work, we demonstrate the power of this algorithm using synthetic x-ray diffraction snapshots from a protein with significant data incompleteness, timing uncertainties, and noise. Our study confirms that NLSA is a suitable approach that effectively mitigates the effects of these artifacts in TR-SFX data and recovers accurate structural dynamics information hidden in such data.

Clustering time-evolving networks using the spatiotemporal graph Laplacian.

Time-evolving graphs arise frequently when modeling complex dynamical systems such as social networks, traffic flow, and biological processes. Developing techniques to identify and analyze communities in these time-varying graph structures is an important challenge. In this work, we generalize existing spectral clustering algorithms from static to dynamic graphs using canonical correlation analysis to capture the temporal evolution of clusters. Based on this extended canonical correlation framework, we define the spatiotemporal graph Laplacian and investigate its spectral properties. We connect these concepts to dynamical systems theory via transfer operators and illustrate the advantages of our method on benchmark graphs by comparison with existing methods. We show that the spatiotemporal graph Laplacian allows for a clear interpretation of cluster structure evolution over time for directed and undirected graphs.