Complex Dynamical Systems Research Articles

Determining the influence of higher harmonics of nonlinear technological load in dynamic action systems

This paper considers the influence of higher harmonics in dynamic action systems due to their complex movement in the process of interaction with the technological load. The object of research is the process of propagation of oscillations in complex dynamic systems. One of the problems in the application of oscillatory processes is the consideration of higher harmonics in the overall movement of systems. To solve the problem, the idea of using a hybrid model that takes into account both discrete and distributed parameters was proposed. The resulting mathematical discrete model in the analytical equations of motion of the dynamic system preserves continuous properties in the form of wave coefficients. These coefficients in their analytical form take into account the contribution of higher harmonics of both the reactive (elastic-inertial) and active (dissipative) components of the resistance force. The studies were carried out on a model of a plant with a multimode spectrum of oscillations and a nonlinear dynamic system, which is a system with piecewise linear characteristics.A series of experimental studies with a wide variation of the change in the frequency of oscillations was carried out on the installation with a multimode spectrum of oscillations. Zones of manifestation of higher harmonics along the vertical axis of force action were revealed. The given spectrum at the exciter frequency of 35 Hz showed the manifestation of the spectrum component (around 70 Hz) along the X axis, which is an important result for practical application. For a system with piecewise linear characteristics, the manifestation of multimode, which manifests itself in the form of subharmonic and superharmonic oscillations, was determined. The contribution of each harmonic is determined by applying the obtained dependences. The results were used in the development of algorithms and calculation methods of a new class of dynamic action systems taking into account the contribution of higher harmonics

Dynamic development of cohesive devices in English as a second language writing

Abstract The dearth of research examining the progression of cohesion in L2 writing through a time-series research design is evident. Therefore, the current study employs the Complex Dynamic Systems Theory to explore the evolution of cohesive devices in L2 writing. Thirty advanced-level L2 writers from a US university participated over a semester, providing 210 written samples at seven measurement points. Analysis of these samples, utilizing 40 cohesion indices from the Tool for the Automatic Analysis of Cohesion, revealed significant improvement in eight cohesion indices (three local, four global, and one text cohesion indices) with large effect sizes. However, time-series analyses indicated nonlinear trends and variability. Additionally, a positive association was found between two local cohesion indices (lexical and semantic overlap) at the initial and final measurement points. The findings demonstrate the multifaceted developmental trajectories and complexities evident in L2 learners’ approaches and carry important implications for L2 writing instruction and assessment.

Computational method for obtaining solitary wave solutions of the (2+1)-dimensional AKNS equation and their physical significance

This study employs precise, accurate, and efficient analytical and numerical techniques to obtain novel and accurate solitary wave solutions for the (2+1)-dimensional Ablowitz–Kaup–Newell–Segur (AKNS) equation. The Khater II (Khat II) method and extended cubic-B-spline (ECBS) scheme are utilized as recent computational and accurate numerical techniques, respectively, for investigating the AKNS equation and constructing highly precise solitary wave solutions. The stability characteristics of the obtained solutions are also analyzed to ensure their applicability. These solutions are characterized by their peak amplitudes, wave speeds, and widths. Through comparisons with previous numerical techniques, our proposed approach demonstrates superior effectiveness and reliability. The research is significant due to the application of the (2+1)-dimensional AKNS equation in modeling various physical phenomena, such as nonlinear optics, water waves, and plasma physics. The precise and efficient determination of solitary wave solutions not only enhances the understanding of these phenomena but also provides a valuable framework for practical applications. The results have substantial implications for comprehending complex wave dynamics in physical systems and serve as a valuable tool for further research and analysis in the field of wave dynamics.

Theory of Center‐Line Slope in 2D Electronic Spectroscopy with Static Disorder

Abstract2D electronic spectroscopy (2DES) is a powerful tool for investigating the dynamics of complex systems. However, analyzing the resulting spectra can be challenging, and thus may require the use of theoretical modeling techniques. The center‐line slope (CLS) method is one of such approaches, which aims to extract the time correlation function (TCF) from 2DES with minimal error. Since static disorder is widely observed in complex systems, it may be interesting to ask whether the CLS approach still work in the presence of the static disorder. In this paper, the effect of the static disorder on the TCF obtained through the CLS method is investigated. It is found that the steady‐state value of the CLS increases monotonically with respect to the static disorder, which suggests that the amplitude of the static disorder can be determined using the CLS in the long‐time limit. Additionally, as the static disorder rises, the decay rate of the CLS first decreases to a certain value and remains at this value until the static disorder is sufficiently large. Afterward, the CLS begins to fluctuate significantly and thus results in obtaining the decay rate through the CLS method unreliable. Based on these discoveries, the authors propose a method to fix the error and obtain the TCF. The findings may pave the way for obtaining reliable system‐bath information by analyzing 2DES in the practical situations.

Closed-Loop Stability of a Non-Minimum Phase Quadruple Tank System Using a Nonlinear Model Predictive Controller with EKF

The dynamics of a quadruple tank system (QTS) represent an extensive class of multivariate nonlinear uncertain systems found in the industry. It has been established that changes in split fractions affect the transmission zero location, thereby altering the operating conditions between the minimum and non-minimum phase regions. The latter is difficult to control as more fluid flows into the two upper tanks than into the two bottom tanks, resulting in competing effects between the initial and final system responses. This attribute, alongside nonlinearity, uncertainties, constraints, and a multivariate nature, can degrade closed-loop system performance, leading to instability. In this study, we addressed the aforementioned challenges by designing controllers for the regulation of the water flow in the two bottom tanks of the QTS. For comparative analysis, three controller algorithms—a nonlinear model predictive controller (NMPC), NMPC augmented with an extended Kalman filter (i.e., NMPC-EKF) and linear model predictive controller (LMPC)—were considered in the analysis and design of the control mechanism for the quadruple water level system in a non-minimum phase condition via the Matrix Laboratory (MATLAB) simulation package environment. The simulated and real-time results in the closed loop were analyzed, and the controller performances were considered based on faster setpoint responses, less oscillation, settling time, overshoot, and smaller integral absolute error (IAE) and integral square error (ISE) under various operational conditions. The study showed that the NMPC, when augmented with an EKF, is effective for the control of a QTS in the non-minimum phase and could be designed for more complex, nonlinear, and multivariable dynamics systems, even in the presence of constraints.

The theory of dynamical systems of conflict in the framework of functional analysis

In this article, we give an introduction to the mathematical setting of problems related to the phenomenon of conflict in terms of constructions in Hilbert spaces. The struggle (conflict, game) between opponents (adversaries, players) will be represented by operator transformations of vectors in Hilbert spaces and probabilistic distributions on the territory of life resources. The phenomenon of conflict as a contradiction between opponents appears in mathematical terms as an intersection the domains of definition for operators and overlapping of corresponding measures. Conflict interaction between opponents in the physical sense is described by the specific transformation of states in a Hilbert space. In turn, this is a mapping that changes the spectral measurements. Thus, a complex dynamical system arises, which we call a dynamical system of conflict. Then the following main problems arise as fundamental questions. What reasonable law of engagement (game or war) should be adopted to resolve the initial intersections? What is a fair limiting distribution of the resource territory? In a more general formulation, solving conflict problems means the detailed describing of all possible outcomes on opponents states of the type: victories, defeats, states of equilibrium, compromises as fixed points together with their basins of attraction.

Processing misconceptions: dynamic systems perspectives on thinking and learning

The study of complex dynamic systems is central to biology. In this essay, I argue that thinking and learning can also be understood as phenomena that emerge from the continuous interactivity of dynamic systems. I first present and apply core concepts of dynamic systems theories to both biological and cognitive systems. I then use these ideas to explain how a dynamic systems perspective can recast the way we think about misconceptions, a central concept in the field of education research. Rather than model misconceptions as object-like entities that students either have or do not have, misconceptions can be modeled as patterns that emerge from continuous cognitive processes. I end by discussing how adopting a dynamic systems perspective suggests a need for research that uses methods designed to study processes in time and can inspire educators to embrace and value variation and fluctuation in students’ thinking and learning.

How the Complexity of Psychological Processes Reframes the Issue of Reproducibility in Psychological Science

In the past decade, various recommendations have been published to enhance the methodological rigor and publication standards in psychological science. However, adhering to these recommendations may have limited impact on the reproducibility of causal effects as long as psychological phenomena continue to be viewed as decomposable into separate and additive statistical structures of causal relationships. In this article, we show that (a) psychological phenomena are patterns emerging from nondecomposable and nonisolable complex processes that obey idiosyncratic nonlinear dynamics, (b) these processual features jeopardize the chances of standard reproducibility of statistical results, and (c) these features call on researchers to reconsider what can and should be reproduced, that is, the psychological processes per se, and the signatures of their complexity and dynamics. Accordingly, we argue for a greater consideration of process causality of psychological phenomena reflected by key properties of complex dynamical systems (CDSs). This implies developing and testing formal models of psychological dynamics, which can be implemented by computer simulation. The scope of the CDS paradigm and its convergences with other paradigms are discussed regarding the reproducibility issue. Ironically, the CDS approach could account for both reproducibility and nonreproducibility of the statistical effects usually sought in mainstream psychological science.

Estimating dynamic individual coactivation patterns based on densely sampled resting-state fMRI data and utilizing it for better subject identification.

As a complex dynamic system, the brain exhibits spatially organized recurring patterns of activity over time. Coactivation patterns (CAPs), which analyzes data from each single frame, have been utilized to detect transient brain activity states recently. However, previous CAP analyses have been conducted at the group level, which might neglect meaningful individual differences. Here, we estimated individual CAP states at both subject- and scan-level based on a densely sampled dataset: Midnight Scan Club. We used differential identifiability, which measures the gap between intra- and inter-subject similarity, to evaluate individual differences. We found individual CAPs at the subject-level achieved the best fingerprinting ability by maintaining high intra-subject similarity and enlarging inter-subject differences, and brain regions of association networks mainly contributed to the identifiability. On the other hand, scan-level CAP states were unstable across scans for the same participant. Expectedly, we found subject-specific CAPs became more reliable and discriminative with more data (i.e., longer duration). As the acquisition time of each participant is limited in practice, our results recommend a data collection strategy that collects more scans with appropriate duration (e.g., 12 ~ 15min/scan) to obtain more reliable subject-specific CAPs, when total acquisition time is fixed (e.g., 150min). In summary, this work has constructed reliable subject-specific CAP states with meaningful individual differences, and recommended an appropriate data collection strategy, which can guide subsequent investigations into individualized brain dynamics.

PTSD Symptom dynamics after the great east japan earthquake: mapping the temporal structure using Dynamic Time Warping

ABSTRACT Background: After the Great East Japan Earthquake [GEJE], approximately 70,000 Japan Ground Self Defense Force [JGSDF] personnel were deployed, risking Post-Traumatic Stress Disorder [PTSD]. The network approach to psychopathology suggests that symptoms may cause and exacerbate each other, resulting in the emergence and maintenance of disorders, including PTSD. It is therefore important to further explore the temporal interplay between symptoms. Most studies assessing the factor structure of the Impact of Event Scale-Revised [IES-R] have used cross-sectional designs. In this study, the structure of the IES-R was re-evaluated while incorporating the temporal interplay between symptoms. Methods: Using Dynamic Time Warping [DTW] the distances between PTSD symptoms on the IES-R were modelled in 1120 JGSDF personnel. Highly correlated symptoms were clustered at the group level using Distatis three-way principal component analyses of the distance matrices. The resulting clusters were compared to the original three subscales of the IES-R using a Confirmatory Factor Analysis (CFA). Results: The DTW analysis yielded four symptom clusters: Intrusion (five items), Hyperarousal (six items), Avoidance (six items), and Dissociation (five items). CFA yielded better fit estimates for this four-factor solution (RMSEA = 0.084, CFI = 0.918, TLI = 0.906), compared to the original three subscales of the IES-R (RMSEA = 0.103, CFI = 0.873, TLI = 0.858). Conclusions: DTW offers a new method of modelling the temporal relationships between symptoms. It yielded four IES-R symptom clusters, which may facilitate understanding of PTSD as a complex dynamic system.

A reduced order model based on adaptive proper orthogonal decomposition incorporated with modal coefficient learning for digital twin in process industry

The digital twin (DT) technology provides a viable and promising direction for improving the level of the production status monitoring and the overall product quality in various fields. However, the accuracy of working condition identification, the timeliness of process adjustment, and the stability of product quality are put forward higher requirements in the process industry, which is characterized by nonlinear, large-scale, and dynamic complex systems. Therefore, it still remains a tricky challenge to construct and maintain an effective and accurate DT model in the process industry. A reduced order model (ROM) with the adaptive updating ability is proposed. The adaptive proper orthogonal decomposition (APOD) is adopted to achieve the continuous iteration and the adaptive optimization of the reduced basis set. Correspondingly, an adaptive learning algorithm based on the least squares support vector regression (LS-SVR) is developed to quickly obtain the modal coefficients and effectively circumvent the prohibitively high computational cost. In this way, the physical field of interest is expressed in a low-dimensional approximation with a high accuracy. The effectiveness of the method is verified by a case study in the process industry. Results show that the proposed model displays a high-precision fitting and a significant time saving for the full order model (FOM).

Exploring male English major’s motivation trajectory through complex dynamic systems theory

Exploring male English major’s motivation trajectory through complex dynamic systems theory

Abstract P1007: Graph Neural Network Analysis Of Dynamic Temporal Relationships Between Chromatin Accessibility And RNA Expression In The Developing Mouse Heart

Mammalian development is a dynamic process that transforms the epigenetic and transcriptomic landscapes of cells as they differentiate into various cell types and tissues. In vertebrates, the heart is the first functioning organ of the embryo, but its development has yet to be fully understood. Using simultaneous scRNA-seq and scATAQ-seq data from three major timepoints (E8.5, E10.5, E16.5) of murine development, we develop a novel approach to analyze the temporal relationship between chromatin accessibility and gene expression across development using RNA velocity and interpretable graph neural network (GNN) models. RNA velocity is a powerful splicing kinetics tool for uncovering directed transcriptional dynamics in complex biological systems, and it infers the direction and rate of change of gene expression in single cells over time by comparing the ratio of unspliced to spliced mRNA reads between adjacent cells. We represent the vectors identified through RNA velocity as a directed graph, thereby transforming the single-cell data with the additional simultaneous ATAC-seq information into an input for a GNN. The GNN then learns the temporal epigenetic and transcriptomic dynamics from the node feature information, ie. scATAC-seq, with the graph structure, ie. RNA velocity vectors, to predict the developmental trajectories of cells. After training of the GNN model, we implement an additional GNN explainer model to analyze it and identify subgraphs, ie. networks of DNA regions, that maximize the mutual information associated with its trajectory predictions. By interpreting the contributions of ATAC peaks in the GNN model, we identify novel regulatory dynamics and trends involved in the separation of distinct cardiac lineages in the developing mouse heart. Ultimately, we provide new insight for future investigation into the temporal relationship between chromatin accessibility and gene expression levels..

Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles

Classical problems in computational physics such as data-driven forecasting and signal reconstruction from sparse sensors have recently seen an explosion in deep neural network (DNN) based algorithmic approaches. However, most DNN models do not provide uncertainty estimates, which are crucial for establishing the trustworthiness of these techniques in downstream decision making tasks and scenarios. In recent years, ensemble-based methods have achieved significant success for the uncertainty quantification in DNNs on a number of benchmark problems. However, their performance on real-world applications remains under-explored. In this work, we present an automated approach to DNN discovery and demonstrate how this may also be utilized for ensemble-based uncertainty quantification. Specifically, we propose the use of a scalable neural and hyperparameter architecture search for discovering an ensemble of DNN models for complex dynamical systems. We highlight how the proposed method not only discovers high-performing neural network ensembles for our tasks, but also quantifies uncertainty seamlessly. This is achieved by using genetic algorithms and Bayesian optimization for sampling the search space of neural network architectures and hyperparameters. Subsequently, a model selection approach is used to identify candidate models for an ensemble set construction. Afterwards, a variance decomposition approach is used to estimate the uncertainty of the predictions from the ensemble. We demonstrate the feasibility of this framework for two tasks — forecasting from historical data and flow reconstruction from sparse sensors for the sea-surface temperature. We demonstrate superior performance from the ensemble in contrast with individual high-performing models and other benchmarks.

Functional annotation of proteins for signaling network inference in non-model species

Molecular biology aims to understand cellular responses and regulatory dynamics in complex biological systems. However, these studies remain challenging in non-model species due to poor functional annotation of regulatory proteins. To overcome this limitation, we develop a multi-layer neural network that determines protein functionality directly from the protein sequence. We annotate kinases and phosphatases in Glycine max. We use the functional annotations from our neural network, Bayesian inference principles, and high resolution phosphoproteomics to infer phosphorylation signaling cascades in soybean exposed to cold, and identify Glyma.10G173000 (TOI5) and Glyma.19G007300 (TOT3) as key temperature regulators. Importantly, the signaling cascade inference does not rely upon known kinase motifs or interaction data, enabling de novo identification of kinase-substrate interactions. Conclusively, our neural network shows generalization and scalability, as such we extend our predictions to Oryza sativa, Zea mays, Sorghum bicolor, and Triticum aestivum. Taken together, we develop a signaling inference approach for non-model species leveraging our predicted kinases and phosphatases.

Managing the Development of Integration Processes in the Innovation Environment of the Region

Relevance. Integration processes form the modern image of the innovative model of the economy through the successful functioning and competent interrelation of the structural elements of the innovation system at the national and regional levels. The control levers of such systems should be effective, and therefore sufficiently diverse and flexible, so as not to limit the system, but to ensure the processes of its functioning and development in the conditions of the singularity of the external environment. A new approach to the study of the problems of innovative development of the region can be offered by the theory of systems with an emphasis on a new understanding of complex self-organizing structures, as well as the concept of open innovation, which allows participants in the innovation process to establish partnerships based on knowledge exchange.The purpose of the study is to find a model solution to the problem of managing the development of integration processes in the innovation environment of the region.The objectives of the study can be formulated as follows: identification of problems of innovative development of the territory; study of theoretical constructions of the development of integration processes in the innovation environment of the region; theoretical justification and development of a model solution for the formation of interaction of stakeholders of the innovation process based on the model of the «Quadruple Innovation Helix».Methodology. The research methodology consists of general scientific methods of cognition, statistical methods, as well as principles and methods of a systematic approach.Results. One of the important problems of the innovative development of the territory is the low level of integration processes that ensure the interaction of regional stakeholders. A model solution to the problem of managing the development of integration processes based on the principles of managing a region as a complex dynamic system and an open innovation model is proposed. This model reveals the problem of balancing the innovative development of the region from the perspective of taking into account the interests of participants in the innovation process.Conclusions. The use of the proposed model allows a comprehensive and systematic approach to the study of the possibilities of effective interaction of participants in the innovation process in the region with the observance of the conditions of balance and synergy as a result for the evaluation of the integration process.

CEBoosting: Online sparse identification of dynamical systems with regime switching by causation entropy boosting.

Regime switching is ubiquitous in many complex dynamical systems with multiscale features, chaotic behavior, and extreme events. In this paper, a causation entropy boosting (CEBoosting) strategy is developed to facilitate the detection of regime switching and the discovery of the dynamics associated with the new regime via online model identification. The causation entropy, which can be efficiently calculated, provides a logic value of each candidate function in a pre-determined library. The reversal of one or a few such causation entropy indicators associated with the model calibrated for the current regime implies the detection of regime switching. Despite the short length of each batch formed by the sequential data, the accumulated value of causation entropy corresponding to a sequence of data batches leads to a robust indicator. With the detected rectification of the model structure, the subsequent parameter estimation becomes a quadratic optimization problem, which is solved using closed analytic formulas. Using the Lorenz 96 model, it is shown that the causation entropy indicator can be efficiently calculated, and the method applies to moderately large dimensional systems. The CEBoosting algorithm is also adaptive to the situation with partial observations. It is shown via a stochastic parameterized model that the CEBoosting strategy can be combined with data assimilation to identify regime switching triggered by the unobserved latent processes. In addition, the CEBoosting method is applied to a nonlinear paradigm model for topographic mean flow interaction, demonstrating the online detection of regime switching in the presence of strong intermittency and extreme events.

Reconstructing dynamics of complex systems from noisy time series with hidden variables

Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high dimensions with partial knowledge of the states. In this paper, we propose a new framework based on a well-designed cost functional, the minimization of which transforms the determination of both the unknown parameters and the unknown state evolution into parameter learning. This method can be conveniently used to reconstruct structures and dynamics of complex networks, even in the presence of noisy disturbances or for intricate parameter dependence. As a demonstration, we successfully apply it to the reconstruction of different dynamics on complex networks such as coupled Lorenz oscillators, neuronal networks, phase oscillators and gene regulation, from only a partial measurement of the node behavior. The simplicity and efficiency of the new framework makes it a powerful alternative to recover system dynamics even in high dimensions, which expects diverse applications in real-world reconstruction.

“Indulge in a Little Chaos”: Assistant Language Teachers’ Cognition and Pedagogical Knowledge Development Through the Lens of Complex Dynamic System Theory

Teacher cognition has been a major topic of interest in applied linguistics as researchers have worked toward “better understanding the fullness of the work of teaching, a fullness that has proved complex and problematic” (Burns et al., 2015, p. 585). This qualitative study draws upon participant interview data in order to analyze and understand language teacher cognition and pedagogical knowledge development of an under-represented cohort—foreign assistant language teachers (ALTs) in Japan. Participants (n=35) were current or former ALTs with 1 to 19 years of experience working as team teachers in Japan. Interview data was transcribed and coded according to six common features of complex dynamic systems: initial condition, unpredictability, nested structure, non-hierarchic networks, feedback loops, and self-organization (Kiss, 2012). Findings show that ALTs’ ability to acquire and operationalize pedagogical knowledge is highly dependent on the maneuver that they must undergo in working within the local Japanese contexts—as opposed to those in their home countries—and in relation to their colleagues who have a variety of individual traits, pedagogical beliefs, and team-teaching practices. This article serves as evidence that language teacher cognition regarding pedagogical knowledge development can be aptly understood through the lens of complex systems theory.

ESG risks to global platinum supply: A case study of Mogalakwena Mine, South Africa

Global demand for metals is expected to continue to grow significantly to 2050, partly driven by the need for climate change mitigation measures that require energy transition metals including platinum group metals (PGMs). The environmental, social and governance (ESG) risks of mining these metals are seldom acknowledged in energy transition scenarios and pose a risk to future metal supply. Multiple ESG drivers at different scales create direct and indirect pressures and risks to a specific mine site and their interactions across scales create complex system dynamics. Although mining companies identify ESG factors as their biggest risks (and opportunities), interdisciplinary mining research is in its infancy and ESG factors are often oversimplified or overlooked. While global studies are important for providing an overview of the industry, and highlighting trends and patterns, they cannot communicate the complexity found at the local scale. This paper describes ESG risks, opportunities, and impacts across nine dimensions (water, energy, biodiversity, waste, air quality, community, social vulnerability, land use, and governance) for Anglo American Platinum’s Mogalakwena PGM mine in South Africa. It provides insight into a developing country African context and an in-depth view of the complex ESG risks around PGM mining in South Africa. Given South Africa hosts 91% of global PGM resources, understanding and addressing these ESG risks is critical for ensuring long-term PGM supply and enabling a just energy transition.