Environmental motivation as a complex dynamic system

Understanding learner agency as a complex dynamic system

Electric power transmission systems are a key infrastructure, and blackouts of these systems have major consequences for the economy and national security. Analyses of blackout data suggest that blackout size distributions have a power law form over much of their range. This result is an indication that blackouts behave as a complex dynamical system. We use a simulation of an upgrading power transmission system to investigate how these complex system dynamics impact the assessment and mitigation of blackout risk. The mitigation of failures in complex systems needs to be approached with care. The mitigation efforts can move the system to a new dynamic equilibrium while remaining near criticality and preserving the power law region. Thus, while the absolute frequency of blackouts of all sizes may be reduced, the underlying forces can still cause the relative frequency of large blackouts to small blackouts to remain the same. Moreover, in some cases, efforts to mitigate small blackouts can even increase the frequency of large blackouts. This result occurs because the large and small blackouts are not mutually independent, but are strongly coupled by the complex dynamics.

Loss and coupling loss factors of two coupled dynamic systems

This article explores the potential offered by complexity theories for understanding language learners’ sense of self and attempts to show how the self might usefully be conceived of as a complex dynamic system. Rather than presenting empirical findings, the article discusses existent research on the self and aims at outlining a conceptual perspective that may inform future studies into the self and possibly other individual learner differences. The article concludes by critically considering the merits of a complexity perspective but also reflecting on the challenges it poses for research.

The article is devoted to the urgent problem of improving the roadway cleaning efficiency. To achieve maximum cleaning efficiency, an optimal pressing force of the brush equipment to the surface being cleaned should be provided. A schematic diagram of a sweeping machine working process as a complex dynamic system was constructed including a basic machine, brush and running equipment, a hydraulic drive, a road surface, as well as a microrelief control device reflecting the effect of the microrelief on the vertical coordinate of the working equipment. A mathematical model of the working process of a sweeping machine is presented. The simulation was carried out using the MATLAB software, Simulink extension. As a result, the dependences of the vertical coordinates and the pressing force of the brush equipment were established. In most cases, the brush positioning control is provided by a standard hydraulic drive; however, when the dimensions of a pothole are large enough, the standard hydraulic pump does not guarantee the required speed of the control device so that the deviations of the vertical coordinate could be compensated. To improve the speed of the brush positioning control device, the standard hydraulic pump was supplemented with an additional pump switching on only at particular periods of time.

Stability is a classical yet active research topic for dynamical systems. Certain operators such as de-noising filters, smoothing filters and many algorithms may be applied iteratively. In many cases, they can be modelled as a complex dynamical system. Due to the errors and noises in acquisition of data, the stability of analysis results is vital to the validity of the analysis. However, little is known about the stability of analysis results in these situations. In this paper, we propose a method for analyzing the stability under iterations of operator. First we give the definition of stability under iterations of operator. We model the dynamics as an complex dynamical system. We introduce the concepts of Fatou and Julia set. We establish the connection of stability to Fatou and Julia set. We define different concepts of quasi-stability including asymptotical, bounded quasi-stability, which generalize the notion of stability. We provide the necessary and sufficient condition for quasi-stability under iteration of affine operator. We present a few results for the quasi-stability based on the concept of Fatou and Julia Set. Finally, we provide the numerical example to illustrate the theory.

Emergence is one of the most essential features of complex systems. This property implies new collective behaviors due to the interaction and self-organization among elements in the system, which cannot be produced by a single unit. It is our task in this Chapter to extensively discuss the basic principle, the paradigm, and the methods of emergence in complex systems based on nonlinear dynamics and statistical physics. We develop the foundation and treatment of emergent processes of complex systems, and then exhibit the emergence dynamics by studying two typical phenomena. The first example is the emergence of collective sustained oscillation in networks of excitable elements and gene regulatory networks. We show the significance of network topology in leading to the collective oscillation. By using the dominant phase-advanced driving method and the function-weight approach, fundamental topologies responsible for generating sustained oscillations such as Winfree loops and motifs are revealed, and the oscillation core and the propagating paths are identified. In this case, the topology reduction is the key procedure in accomplishing the dimension-reduction description of a complex system. In the presence of multiple periodic motions, different rhythmic dynamics will compete and cooperate and eventually make coherent or synchronous motion. Microdynamics indicates a dimension reduction at the onset of synchronization. We will introduce statistical methods to explore the synchronization of complex systems as a non-equilibrium transition. We will give a detailed discussion of the Kuramoto self-consistency approach and the Ott-Antonsen ansatz. The synchronization dynamics of a star-networked coupled oscillators and give the analytical description of the transitions among various ordered macrostates. Finally, we summarize the paradigms of studies of the emergence and complex systems.

Most dynamical systems in real-life applications are usually nonlinear and nonstationary, such as biomechanical systems, neuroscience, healthcare, economics, and engineering. Nowadays, the availability of data makes it possible to investigate and discover the hidden dynamics of target systems. However, numerous concerns arise in modeling and analysis of such systems, including complex system structure, data-inherent uncertainty in observations, poor interpretability, etc. To this end, we will investigate dynamical behaviors by proposing data-driven machine learning and dynamical system techniques. Specifically, we present various approaches for extracting characteristics or patterns that have good interpretability in various complex dynamical system applications.In the first study, we consider a pattern recognition problem in biomechanical system using multivariate human kinematic data and propose data-driven analytical methods to model human movement. We first perform recurrence quantification analysis on the phase space of the kinematic system to visualize and evaluate the recurrence behavior of the folded phase space trajectory. However, this method could miss out the relationship between variables. We therefore introduce a new modeling approach based on the self-expressive assumption to discover the interactions between variables and characterize the patterns of human motion. Our model measures correlations between variables by underlying linear subspaces, which can be further extended to nonlinear subspaces. Based on these correlations, our model improves the classification accuracy by 20% - 30% over other standard state-of-art correlation measurements and clustering methods. In the second study, we consider a specific neuroscience problem, seizure detection, to recognize abnormal brain states by learning from highly nonlinear electroencephalography. Based on dynamical systems theory, Koopman operator theory, and dynamic mode decomposition, we project the complex brain dynamics into an infinite-dimensional linear space, where the intrinsic linear dynamic shares the same dynamical behavior as the original nonlinear dynamical system. We propose a new system measurement to unify the projections in different Koopman spaces. Our measurement indicates the stability of the dynamical system, which represents the system state trajectory with respect to the corresponding attractor. We demonstrate the effectiveness of our approach with a seizure onset detection task. In this case study, our model gives high accuracy with a low false-positive rate. In the last study, we consider dynamical systems with multiple modalities. We design a Koopman-based deep learning network to identify and simplify the intrinsic nonlinear dynamics from different sources/observations of a multi-modal dynamical system. Since these different modalities describe the same system, they jointly share the same intrinsic dynamics. We develop an autoencoder framework with custom loss functions to find proper project functions/operators and to obtain the intrinsic Koopman coordinates. Our framework can reconstruct the original system states based on the joint dynamics. Once the intrinsic linear dynamics is learned, future system states can be predicted by the evolution in the Koopman space. This approach allows us to uncover and linearize the hidden nonlinear dynamics, which enables linear dynamical tools, for example, system control, spectrum analysis, to analyze complex dynamical systems.--Author's abstract

The study of the critical dynamics in complex systems is always interesting yet challenging. Here, we choose financial markets as an example of a complex system, and do comparative analyses of two stock markets—the S&P 500 (USA) and Nikkei 225 (JPN). Our analyses are based on the evolution of cross-correlation structure patterns of short-time epochs for a 32 year period (1985–2016). We identify ‘market states’ as clusters of similar correlation structures, which occur more frequently than by pure chance (randomness). The dynamical transitions between the correlation structures reflect the evolution of the market states. Power mapping method from the random matrix theory is used to suppress the noise on correlation patterns, and an adaptation of the intra-cluster distance method is used to obtain the ‘optimum’ number of market states. We find that the S&P 500 is characterized by four market states and Nikkei 225 by five. We further analyze the co-occurrence of paired market states; the probability of remaining in the same state is much higher than the transition to a different state. The transitions to other states mainly occur among the immediately adjacent states, with a few rare intermittent transitions to the remote states. The state adjacent to the critical state (market crash) may serve as an indicator or a ‘precursor’ for the critical state and this novel method of identifying the long-term precursors may be helpful for constructing the early warning system in financial markets, as well as in other complex systems.

The study on stationary solution of a stochastically complex dynamical system

The author brings a complexity sensibility to the concept of interpretation by conceptualizing an interpretive attitude as both a continual internal striving to understand and organize the multiplicity of experiences and states that emerge in an analytic field and an emergent property of that field—a complex dynamic system in which everything counts. Her interpretive attitude helps her patient to bring more coherence to his internal confusion and chaos. Inevitably, she communicates meaning to him implicitly, and when it seems useful, explicitly, as she strives to bring disparate things together lightly so he can move forward in his life with more freedom and vitality.

Service-life is a widely used reliability index in reliability engineering. For a complex dynamic system for which whole system tests are limited, and there is insufficient information to determine the distribution function of reliability models. Fortunately, the boundaries of lifetime variable can be obtained, which can be incorporated through the theory of interval uncertainty. In this study, a service-life assessment method for complex dynamic systems under interval uncertainty is introduced based on Bayesian networks (BN). Firstly, a dynamic fault tree (DFT) model is built for a system. Based on the comprehensive integration of test data, field data, design data and engineering experience, the lifetime of system units are expressed as interval numbers. Then, a coefficient of variation (COV) method is employed to determine the parameters of life distributions. Finally, the BN method is used to estimate the mean life of the example system, and the service-life of this system is assessed as well. The presented method can be easily used in engineering practice for service-life evaluation of complex dynamic systems under interval uncertainty, where lifetime data is limited.

The aim of this mixed methods case study is to explore EAP (English for Academic Purposes) classes at universities in Kurdistan, North Iraq through two conceptual frameworks: The Actional Phase of The Process model of L2 motivation; (Dörnyei and Ottó, 1998) and Complex Dynamic Systems theory (Larsen-Freeman, 1997). The study explores the relationship between teaching practices and ability grouping on students’ academic motivation, academic self-concept, and classroom engagement seeking both teachers and students’ opinions, beliefs and perspectives. Employing an exploratory sequential research design, a combination of qualitative and quantitative research methodologies was used to analyse data from questionnaires, interviews and classroom observations. A complexity lens highlights the interrelatedness of the three constructs in an emerging educational setting as a complex dynamic system. Moreover, it reveals that several aspects of Dörnyei and Ottó’s (1998) model can be enhanced by and related to the Complex Dynamic Systems framework.

The challenging issues of modelling and controlling complex dynamic systems (CDS) are carefully considered and properly addressed. Qualitative description of most of the parameters of complex dynamic systems results inevitably in fuzziness, complexity and uncertainty. One of the challenges of accepting the operation of any complex dynamic system is the ability to make Decisions so the system runs efficiently and cost effectively. A short but useful historical overview of decision support systems (DSS) is given. The need for new conceptual and advanced models for addressing the challenging issues of CDS is provided. Fuzzy Cognitive Maps (FCMs) as a new modelling approach is briefly described. An illustrative example is provided along with some very interesting promising results.

Background: The study of repetitive (quasi-periodic) spatio-temporal patterns in complex dynamical systems with a well defined spatial structure may be complicated if the recurrent behavior is confined to specific local regions, where it lasts for a limited time. This can decrease the efficacy of recurrence plots (RPs) in recognizing such patterns. It then becomes important to first detect whether repetitive spatio-temporal patterns are present, and if so, where they are located (both in space and time), to facilitate a focused RP analysis approach. This study proposes a novel framework for spatio-temporal detection of local recurrence of a quasi-periodic nature in complex dynamical systems. A motivating application for this framework is the analysis of atrial fibrillation to better understand the heart tissue involved. Methods: The spatio-temporal data observed from the system are decomposed by means of principal component analysis to identify the points in the spatial structure exhibiting quasi-periodic recurrent patterns. The frequency content of the principal components is used to determine if such patterns are present, and the corresponding eigenvectors are used to identify the points associated with those components. Geometric information about proximity of these points is used to cluster them into local regions. A sliding temporal window is used to detect the start and end of each pattern. Results: A first simulation shows how the proposed framework can handle multiple recurrent patterns simultaneously occurring in a spatial structure of a dynamical system. A second simulation shows how the method can handle more complicated patterns like 2D nonlinear spiraling waves, typical of many diffusion processes. The framework is then applied to real data to detect recurrent patterns in wave fronts propagating inside the heart during atrial fibrillation. This analysis can unveil regions of recurrence in the atria that were not visible with standard RP analysis. Conclusion: A novel framework for detecting spatio-temporal repetitive patterns in complex dynamical systems is introduced. It allows retrieve the correct recurrences associated with known 2D traveling waves, while the same information is not visible with standard RP analysis. This framework can be effectively used to investigate recurrence in real dynamical systems as cardiac arrhythmia.