Complex Dynamical Systems Research Articles

Nonideal Incompressible Lattice-Boltzmann Method for Multicomponent Phase Separating Systems

Understanding and predicting the dynamics of complex fluid systems including liquid–liquid phase separation, relevant to both biological and engineered applications, typically uses a nonideal free energy. Introducing such a thermodynamic constraint into the Lattice-Boltzmann Method can be accomplished by altering either the equilibrium distribution function or the external force. The former requires a lengthy parameterization for a free energy of multiple independent variables which becomes cumbersome for more than three components. The latter has been done for a multicomponent compressible system, but a correction term for the force is required to recover the expected conservation equations. This work builds upon the incompressible single component forcing method from He et al. (Journal of Computational Physics, Vol. 152, No. 2, 1999) by deriving and implementing the required force needed to successfully recover the expected mass conservation from a nonideal free energy with an arbitrary number of components. This allows the simulation of more realistic phase separating fluid systems by including many interacting components, which is demonstrated here for up to five components and phases.

Multilevel modeling and control of dynamic systems.

The underlying changes of complex dynamic systems are affected by numerous highly interdependent components with nonlinear interactions and cannot be suitably predicted by merely analyzing their individual parts. Recent technological developments (reducing the size of actuators and sensors, increasing speed and productivity) make it possible to monitor and handle systems on time, even during transient processes. In many practical applications, to effectively study rapidly evolving systems, their structure has to be examined at three levels: Micro-Scale (Short-Term), Meso-Scale (Intermediate-Term), and Macro-Scale (Long-Term). This multiscale framework provides a powerful tool for understanding and managing the intricate dynamics of complex systems. Macro-scale and micro-scale approaches are conventionally utilized in general system modeling and control theory, especially within the fields of networked control and multi-agent systems. By leveraging the meso-scale perspective, it is possible to balance detailed component analysis with overarching system behaviors, thereby enhancing the efficiency and effectiveness of operational strategies in complex systems. This paper presents and discusses a formal meso-level depiction of dynamics and control, assuming a finite number of attractors form and remain stable over time progress. Integral characteristics and dynamics of clusters are defined, simplifying control synthesis while maintaining problem formulation. A significant challenge is the model error due to changing cluster structures linked to randomized estimation and optimization algorithms valid under unknown disturbances. To demonstrate the practicality of this framework, the approach is applied to control tasks of a group of robots, leading to scalable and effective control strategies.

Hypergraph modeling of complex interactions: Applications from human musculoskeletal structures to complex system dynamics.

The musculoskeletal network is a complex system of different types of nodes and edges interacting with each other. Although there is a wealth of knowledge about the anatomical components of the human body and the connections between them, the interdependence of these components as a system remains largely unexplored. This study aims to understand the structure of musculoskeletal networks by using hypergraphs as a model of the musculoskeletal system with many-to-many connections. We used both pairwise and hypergraph-based embedding methods to learn the connectivity of muscles. Experiments demonstrated the superiority of the proposed hypergraph-based method over pairwise methods in distinguishing the specific roles of the muscles connecting different body parts.

Modular Modeling of a Half-Vehicle System Using Generalized Receptance Coupling and Frequency-Based Substructuring (GRCFBS)

This paper presents an advanced modular modeling approach for vertical vibration analysis of dynamic systems using the Generalized Receptance Coupling and Frequency-Based Substructuring (GRCFBS) method. The focus is on a four-DoF half-vehicle model comprising three key subsystems: front suspension, rear suspension, and the vehicle’s trimmed body. The proposed technique is designed to predict dynamic responses in reconfigurable systems across various applications, including automotive, robotics, mechanical machinery, and aerospace structures. By coupling the receptance matrices (FRFs) of individual vehicle modules, the overall system receptance matrix is efficiently derived in a disassembled configuration. Two generalized coupling methods, originally developed by Jetmundsen and D.D. Klerk, are employed to determine the complete vehicle’s receptance matrix from its subsystems. Validation is achieved by comparing the results with established methods, such as direct solution and modal analysis, demonstrating high accuracy and reliability for complex dynamic systems. This modular approach allows for the creation of reduced-order models focused on key measurement points without the need for detailed system representation. The method offers significant advantages in early-stage vehicle development, providing critical insights into system vibration behavior.

Optimizing inverted pendulum control: Integrating neural network adaptability

This study explores the implementation and efficacy of a neural network controller for an inverted pendulum system, contrasting it with traditional state feedback control. Initially, state feedback control exhibited limitations in managing complex system dynamics. Subsequently, a neural network controller was developed, trained using datasets from both uncontrolled and refined state space models. The refined model yielded lower training loss and superior control performance. This research demonstrates the neural network controllers enhanced adaptability and precision, offering significant improvements over traditional methods in controlling dynamic systems like inverted pendulums.

Automated control complex of agrotechnology in precision farming

The paper presents a project of an automated complex for managing agricultural technology. The complex consists of two inseparable components, a control unit and an executive robotic technological machine. The control unit implements the modern theory of controlling a complex dynamic system, which is an agricultural field with sowing crops. The main distinctive feature of the proposed management theory is that the object of management is an agrocenoses, which includes sowing crops and weeds. This feature is transferred to the executive technological machine, through which the simultaneous application of mineral fertilizers and herbicide treatment is carried out. At the same time, the formation of optimal technological operations is carried out on the basis of Earth remote sensing data. Based on these data, the parameters of the state of the agrocenoses are assessed, and the resulting estimates are system-wide feedback through which agricultural technology is managed. The presented complex is of interest to specialists developing individual components of modern precision farming systems.

STEWART PLATFORM MULTIDIMENSIONAL TRACKING CONTROL SYSTEM SYNTHESIS

Context. Creating guaranteed competitive motion control systems for complex multidimensional moving objects, including unstable ones, that operate under random controlled and uncontrolled disturbing factors, with minimal design costs, is one of the main requirements for achieving success in this class devices market. Additionally, to meet modern demands for the accuracy of motion control processes along a specified or programmed trajectory, it is essential to synthesize an optimal control system based on experimental data obtained under conditions closely approximating the real operating mode of the test object. Objective. The research presented in this article aims to synthesize an optimal tracking control system for the Stewart platform’s working surface motion, taking into account its multidimensional dynamic model. Method. The article employs a method of a multidimensional tracking control system structural transformation into an equivalent stabilization system for the motion of a multidimensional control object. It also utilizes an algorithm for synthesizing optimal stabilization systems for dynamic objects, whether stable or not, under stationary random external disturbances. The justified algorithm for synthesizing optimal stochastic stabilization systems is constructed using operations such as addition and multiplication of polynomial and fractional-rational matrices, Wiener factorization, Wiener separation of fractional-rational matrices, and the calculation of dispersion integrals. Results. As a result of the conducted research, the problem of defining the concept of analytical design for a Stewart platform’s optimal motion control system has been formalized. The results include the derived transformation equations from the tracking control system to the equivalent stabilization system of the Stewart platform’s working surface motion. Furthermore, the structure and parameters of the main controller transfer function matrix for of this control system have been determined. Conclusions. The justified use of the analytical design concept for the Stewart platform’s working surface optimal motion control system formalizes and significantly simplifies the solution to the problem of synthesizing complex dynamic systems, applying the developed technology presented in [1]. The obtained structure and parameters of the Stewart platform’s working surface motion control system main controller, which is divided into three components W1, W2, and W3, improve the tracking quality of the program signal vector, account for the cross-connections within the Stewart platform, and increase the accuracy of executing the specified trajectory by increasing the degrees of freedom in choosing the controller structure

Symmetry in Signals: A New Insight

Symmetry is a fundamental property of many natural systems, which is observable through signals. In most out-of-equilibrium complex dynamic systems, the observed signals are asymmetric. However, for certain operating modes, some systems have demonstrated a resurgence of symmetry in their signals. Research has naturally focused on examining time invariance to quantify this symmetry. Measures based on the statistical and harmonic properties of signals have been proposed, but most of them focused on harmonic distortion without explicitly measuring symmetry. This paper introduces a new mathematical framework based on group theory for analyzing signal symmetry beyond time invariance. It presents new indicators to evaluate different types of symmetry in non-stochastic symmetric signals. Both periodic and non-periodic symmetric signals are analyzed to formalize the problem. The study raises critical questions about the completeness of symmetry in signals and proposes a new classification for periodic and non-periodic signals that goes beyond the traditional classification based on Fourier coefficients. Furthermore, new measures such as “symmetrometry” and “distorsymmetry” are introduced to quantify symmetry. These measures outperform traditional indicators like Total Harmonic Distortion (THD) and provide a more accurate measurement of symmetry in complex signals from applications where duty cycle plays a major role.

Embracing complexity in psychiatry-from reductionistic to systems approaches.

The understanding and treatment of psychiatric disorders present unique challenges due to these conditions' multifaceted nature, comprising dynamic interactions between biological, psychological, social, and environmental factors. Traditional reductionistic approaches often simplify these conditions into linear cause-and-effect relationships, overlooking the complexity and interconnectedness inherent in psychiatric disorders. Advances in complex systems approaches provide a comprehensive framework to capture and quantify the non-linear and emergent properties of psychiatric disorders. This Personal View emphasises the importance of identifying rules for generative models that govern brain and behaviour over time, which might contribute to personalised assessments and interventions for psychiatric disorders. For instance, mood fluctuations in bipolar disorder can be understood through dynamical systems modelling, which identifies modifiable parameters, such as circadian disruption, that can be addressed through targeted therapies such as light therapy. Similarly, recognition of depression as an emergent property arising from complex interactions highlights the need for integrated treatment strategies that enhance adaptive reactions in the individual. A framework for quantifying multilevel interactions and network dynamics can help researchers and clinicians to understand the interplay between neural circuits, behaviours, and social contexts. Probabilistic models and self-organisation concepts contribute to building concrete dynamical systems models of mental disorders, facilitating early identification of risk states and promoting resilience through adaptive interventions delivered with optimal timing. Embracing these complex systems approaches in psychiatry could capture the true nature of psychiatric disorders as properties of a dynamic complex system and not the manifestation of any lesion or insult. This line of thinking might improve diagnosis and treatment, offering new hope for individuals affected by psychiatric conditions and paving the way for more effective, personalised mental health care.

Comparative Real-Time Study of Three Enhanced Control Strategies Applied to Dynamic Process Systems

In this study, a comparative analysis of three different control methods for precise, real-time control of a complex dynamic double-tank liquid level process system was performed. Since the system in question has a time-delayed structure, feedforward proportional integral (FF-PI) control and cascaded nonlinear feedforward proportional integral delayed (CNPIR) controllers were tested on the process system. While the FF-PI controller improved the response time of the system, it showed limitations in handling external disturbances and nonlinearities. On the other hand, the CNPIR controller showed better improvements in control accuracy and lower overshoot compared to the FF-PI controller. Since the process system has a nonlinear model and is affected by external disturbances, these two controllers were inadequate in this study when compared to the fractional order adaptive proportional integral derivative sliding mode controller (FO-APIDSMC). The FO-APIDSMC controller provided fairly good performance in both tracking accuracy and disturbance rejection control for non-chattering, fast finite-time convergence, increased robustness, and uncertain dynamic processes. Experimental results reveal that the FO-APIDSMC controller achieves superior minimized tracking error and outperforms the FF-PI and CNPIR controllers by effectively handling uncertainties and external disturbances.

Pipe production cost management model based on graph theory

The pipe production process is a complex dynamical system with a significant number of production operations and interconnected cost localization centres. Purpose. To develop a mathematical model of the process of handling analytical information of a pipe enterprise using graph theory for the needs of cost management at each production stage. Methodology. Technological flow charts of the production job, where the list of mandatory activities and routing of the operating process are indicated, were used to organize cost accounting by operational centres of their localization with the help of computer modelling elements, namely the graph theory. The work used a complex of research methods, including analysis and scientific synthesis of scientific and technical information; theoretical studies; methods of mathematical and computer modelling, engineering developments. Findings. The cost accounting process is represented by a directed hypergraph. Each production operation is associated with a graph vertex. Each vertex is assigned to a series of interrelated marks: type of technological operation; weight factor; the value of direct costs for the operation; the value of indirect costs for the operation; the expense factor. The initial state of the hypergraph is specified by means of its initial marking, which corresponds to the set cipher of the batch of pipes and its weight. Further execution of the marked hypergraph is performed by running the allowed vertices. Marking of the graph ends if all the information from the technological flow charts of pipe products has been used. Originality. A model of cost management by operational centres is proposed which will allow dividing the prime cost of pipes which differ according to the production technology. It is recommended to rank pipe products within each technologically similar group for an economically feasible allocation of costs between batches of pipes. The proposed process model of processing analytical information of the pipe enterprise using graph theory will allow providing data governance as for the prime cost of each individual batch of pipe products, will contribute to the improvement in the order generation procedure taking into account the acquired information, and will allow making the appropriate adjustments when making management decisions. Practical value. Calculation of expenses for production operations allows one to identify the most cost-intensive of them. Relying on the results of the calculation, the enterprise management has the opportunity to manage costs at any stage of the production process. Moreover, the model allows determining the amount of consumed metal for each production operation, which is relevant for pipe enterprises. It is appropriate to focus further scientific developments in this direction on the possibility of managing non-manufacturing cost with the help of mathematical models in economics to optimize the supply and sales activities of the enterprise.

Resilience Components in Mexican Whale-Watching Regulation

Whale watching (WW) is a growing tourist activity that is at risk of becoming unsustainable. Legislation regarding WW must mitigate adverse effects on species and address the dynamics of complex systems. This study proposes analyzing this interaction using a socio-ecological resilience framework, considering both social and ecological components. Resilient governance is characterized by four features: flexibility to respond to change, adaptability, multi-level governance, and participation. The aim of this study was to assess how Mexican WW regulations contribute to the resilience of the socio-ecosystem through a literature review on compliance with the regulations and the presence of resilience elements in the regulations. Non-compliance with 12 guidelines was identified, with vessel crowding, distance, and unauthorized vessels being the most frequently reported issues. The analysis of the regulations revealed the presence of all four elements of resilient governance; however, participation is limited to certain key stakeholders, which undermines whale conservation due to non-compliance. In conclusion, the Mexican regulations contribute to resilient governance; however, to ensure whale conservation and socio-ecological resilience, it is essential that all involved parties understand their roles and actively participate in decision-making processes.

Exploring the perceived dynamic system driving inequities in the community obesogenic environment

Abstract Introduction Persons in socioeconomically disadvantaged situations (PSEDS) are more susceptible and disproportionally exposed to obesogenic environments, resulting in poorer dietary outcomes and lower levels of physical activity. This study aimed to map the complex dynamic system within the community obesogenic environment driving unhealthy eating and insufficient physical activity among PSEDS in Flanders, and to identify potential local actions. Methods Participatory group model building (GMB), a qualitative system dynamics method, was used to engage PSEDS (n = 7), local decision makers (n = 7) and local stakeholders (n = 5) in two Flemish municipalities. A two-day GMB session was held in each municipality during which a causal loop diagram (CLD) was created and potential local actions were identified by considering causal pathways and reinforcing loops in the system. Results The CLD was designed around two main variables (i) healthy eating and (ii) physical activity among PSEDS. Seven sub-systems could be identified: 1) social environment, 2) facilities and activities, 3) mobility options, 4) information, 5) affordability, 6) safety (specifically for physical activity), and 7) industry and advertisement (specifically for eating behaviour). Several actions to improve the local environment to promote eating behaviour and physical activity among PSEDS were identified. Conclusions The CLD illustrates the complex interactions between individual and environmental determinants contributing to inequalities in eating behaviour and physical activity by including multiple perspectives of community members in socioeconomically disadvantaged situations, local decision makers and local stakeholders. Both the participatory GMB approach and the final CLD visualization can provide the basis for planning local actions for promoting healthy eating behaviour and physical activity among PSEDS. Key messages • Group model building is an effective approach to explore and understand a dynamic complex system through a shared understanding among diverse stakeholders. • A systems approach is valuable to provide a more comprehensive and context-specific understanding of the perceived factors contributing to inequities in the obesogenic environment.

Dynamics analysis of green supply chain under the conditions of demand uncertainty and blockchain technology

This research investigates the implications of incorporating blockchain technology into the process of making decisions for green supply chains, particularly under conditions of demand uncertainty. A model was formulated to encompass both environmentally friendly products enabled by blockchain technology and those without such enabling technology. The study further explores the optimal method of introducing green input in a duopoly market using game theory. It also examines how consumer uncertainty about green products and acceptance of the technical parameters of blockchain influence this strategy. The findings suggest that increased consumer uncertainty can, in some instances, motivate manufacturers to enhance the eco-friendliness of their products and improve supply chain performance. However, the universal adoption of blockchain does not necessarily ensure better results; on the contrary, it may compromise product sustainability while enhancing supply chain profitability. Moreover, research has indicated that products enabled by blockchain typically have lower prices, thereby offering potential benefits to consumers when acceptance of sustainable energy solutions is high or uncertain. Additionally, this paper analyzes the impact of changes in green supply chain decision-making on system reliability. This involves exploring the relationship between decision parameters and consumer reluctance towards sustainable products and the adoption of blockchain technology. To ensure stable market competition in dynamic complex systems, research shows that feedback control technology can effectively regulate unpredictable behavior.

Stationary correlation pattern in highly non-stationary MEG recordings of healthy subjects and its relation to former EEG studies.

In this study, we analyze magnetoencephalographic (MEG) recordings from 48 clinically healthy subjects obtained from the Human Connectome Project (HCP) while they performed a working memory task and a motor task. Our results reveal a well-developed, stable interrelation pattern that spans the entire scalp and is nearly universal, being almost task- and subject-independent. Additionally, we demonstrate that this pattern closely resembles a stationary correlation pattern (SCP) observed in EEG signals under various physiological and pathological conditions (the distribution of Pearson correlations are centered at about 0.75). Furthermore, we identify the most effective EEG reference for studying the brain's functional network derived from lag-zero cross-correlations. We contextualize these findings within the theory of complex dynamical systems operating near a critical point of a phase transition.

Changes in Language Learners’ Affect: A Complex Dynamic Systems Theory Perspective

AbstractThis study investigated changes in motivation, self‐efficacy beliefs, and a range of emotions, including enjoyment, hope, pride, curiosity, anxiety, boredom, apathy, confusion, and shame, from a complex dynamic systems theory (CDST) perspective over a 2‐year period in the Hungarian English as a Foreign Language (EFL) context. Using the same questionnaire, we collected data four times throughout 4 semesters from 101 participants studying English in two Hungarian high schools. For data analysis, we used latent growth curve modeling (LGCM) to detect the group‐level changes in learners’ motivation, self‐efficacy, and emotions. We also employed dynamic cluster analysis to identify trends in learners’ trajectories regarding these variables. In our panel data, linear models described the data well concerning the ought‐to second language (L2) self, language learning experience, boredom, apathy, and confusion, and for enjoyment, curiosity, anxiety, and shame, nonlinear models had the best fit. We could also identify trajectories depicting attractor states and learner paths that featured influences of perturbations.

Generative learning for forecasting the dynamics of high-dimensional complex systems

We introduce generative models for accelerating simulations of high-dimensional systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are down sampled to a lower dimensional manifold that is evolved through an auto-regressive attention mechanism. In turn, Bayesian diffusion models, that map this low-dimensional manifold onto its corresponding high-dimensional space, operate on batches of physics correlated, time sequences of data and capture the statistics of the system dynamics. We demonstrate the capabilities and drawbacks of G-LED in simulations of several benchmark systems, including the Kuramoto-Sivashinsky (KS) equation, two-dimensional high Reynolds number flow over a backward-facing step, and simulations of three-dimensional turbulent channel flow. The results demonstrate that generative learning offers new frontiers for the accurate forecasting of the statistical properties of high-dimensional systems at a reduced computational cost.

FMO-LC-TDDFTB method for excited states of large molecular assemblies in the strong light-matter coupling regime.

We present a new methodology to calculate the strong light-matter coupling between photonic modes in microcavities and large molecular aggregates that consist of hundreds of molecular fragments. To this end, we combine our fragment molecular orbital long-range corrected time-dependent density functional tight-binding methodology with a generalized Tavis-Cummings Hamiltonian. We employ an excitonic Hamiltonian, which is built from a quasi-diabatic basis that is constructed from locally excited and charge-transfer states of all molecular fragments. To calculate polaritonic states, we extend our quasi-diabatic basis to include photonic states of a microcavity and derive and implement the couplings between the locally excited states and the cavity states and built a Tavis-Cummings Hamiltonian that incorporates the intermolecular excitonic couplings. Subsequently, we demonstrate the capability of our methodology by simulating the influence of the electric field polarization on the polaritonic spectra for a tetracene aggregate of 125 monomers. Furthermore, we investigate the dependence of the splitting of the upper and lower polaritonic branches on the system size by comparing the spectra of five different tetracene clusters. In addition, we investigate the polariton dispersion of a large tetracene aggregate for electric field polarizations in the x, y, and z directions. Our new methodology can facilitate the future study of exciton dynamics in complex molecular systems, which consist of up to hundreds of molecules that are influenced by strong light-matter coupling to microcavities.

What do trees reveal about the sliding of the lateral moraine of the Belvedere Glacier (western Italian Alps)?

The debris-covered Belvedere Glacier is an iconic place for investigating glacier dynamics and geomorphological processes typical of high mountain environments. Moreover, being located in an area highly suited to tourism, glacial and geomorphological hazards can evolve into risk scenarios. Particular attention has been paid during this research to the surge-type event that occurred at the beginning of the 21st century, and to the recent sliding of a lateral moraine nearby the chairlift station. Tree sampling was performed (19 trees on the lateral moraine; 10 undisturbed trees), and the results were compared with morphometric measurements on orthophotos of different years. Besides sampling trunks, the six available exposed roots (13 samples) from a tree located along the sliding niche were sampled to identify the exposure time. Morphometric measurements of the touristic trail dislocation indicate a sliding rate of 1.87 m/y – 1.98 m/y (2018–2023), while the regression rate of the sliding niche is 1.70 m/y (2021–2023). The age of trees along the trench is variable (14–49 years), as is the signal of compression wood, enhancing differentially the passage of the surge wave and the subsequent glacier downwasting. The beginning of root exposure occurred between 2017 and 2019, before the effective evidence of large fractures in the ground. Moreover, the roots show traumatic resin ducts in the period between 2020 and 2022, confirming the tree disturbance. In conclusion, the investigated events are recorded differentially in the sampled trees, especially in roots, anticipating the actual commencement of ground failure. A multidisciplinary approach, including remote sensing, field survey, and dendrogeomorphological analysis is essential to define the dynamics of complex systems.

Study abroad experiences in homestay: where complexity, dynamicity, and individuality stay

Abstract Informed by Complex Dynamic Systems Theory, this study examines the nature of homestay as a situated language learning site, with an eye toward the development of American student guests and Chinese host families’ homestay experiences within the larger context of the study abroad (SA) program and local community. Drawing on data collected from host families and student guests, this study discovers benefits, conflicts, and co-adaptations in homestay; the evolution of host families’ dispositions toward homestay; student guests’ proficiency gains and interactions with hosts and locals; and contextual factors that influence the proficiency gains and interactions. The findings reveal that homestay is a dynamic, self-evolving subsystem, which constantly interacts with other dynamic subsystems, such as the SA program and local community, within the complex social ecosystem of the entire SA environment. This study also provides suggestions for the design and management of the homestay component in the SA program and future research.