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The temperature dependence of spectra can reveal important insights into the structural and dynamical behavior of the system being probed. In the case of linear spectra, this has been exploited to investigate the thermodynamic driving forces governing the spectral response. Indeed, the temperature derivative of a spectrum can be used to obtain effective energetic and entropic profiles as a function of the measured frequency. The former can further be used to predict the temperature-dependent spectrum via a van't Hoff relation. However, these approaches are not directly applicable to nonlinear, complex-valued spectra, such as vibrational sum-frequency generation (SFG) or two-dimensional infrared (2D-IR) photon echo spectra. Here, we show how the energetic and entropic driving forces governing such nonlinear spectra can be determined and used within a generalized van't Hoff relation to predict their temperature dependence. The central idea is to allow the underlying energetic profiles to themselves be complex-valued. We illustrate this approach for 2D-IR spectra of water and SFG spectra of the air–water interface and demonstrate the accuracy of the generalized van't Hoff relationship and its implications for the origin of temperature-dependent spectral changes. [ABSTRACT FROM AUTHOR]

The authors previously developed a divide-and-conquer (DC)-based non-local excited-state calculation method for large systems using dynamical polarizability [Nakai and Yoshikawa, J. Chem. Phys. 146, 124123 (2017)]. This method evaluates the excitation energies and oscillator strengths using information on the dynamical polarizability poles. This article proposes a novel analysis of the previously developed method to obtain further configuration information on excited states, including excitation and de-excitation coefficients of each excitation configuration. Numerical applications to simple molecules, such as ethylene, hydrogen molecule, ammonia, and pyridazine, confirmed that the proposed analysis could accurately reproduce the excitation and de-excitation coefficients. The combination with the DC scheme enables both the local and non-local excited states of large systems with an excited nature to be treated. [ABSTRACT FROM AUTHOR]

Liquid–liquid phase separation in biology has recently been shown to play a major role in the spatial control of biomolecular components within the cell. However, as they are phase transitions, these processes also display nontrivial dynamics. A model phase-separating system of DNA nanostars provides unique access to nucleation physics in a biomolecular context, as phase separation is driven near room temperature by highly thermo-responsive DNA hybridization and at modest DNA concentrations. By measuring the delay time for phase-separated droplets to appear, we demonstrate that the dynamics of DNA nanostar phase separation reflect that of a metastable binary mixture of patchy particles. For sufficiently deep temperature quenches, droplets undergo spinodal decomposition and grow spontaneously, driven by Brownian motion and coalescence of phase-separated droplets, as confirmed by comparing experimental measurements to particle-based simulations. Near the coexistence boundary, droplet growth slows substantially, indicative of a nucleation process. The temperature dependence of droplet appearance times can be predicted by a classical nucleation picture with mean field exponents and demonstrates that a theory previously used to predict equilibrium phase diagrams can also distinguish spinodal and nucleation dynamical regimes. These dynamical principles are relevant to behaviors associated with liquid–liquid phase separating systems, such as their spatial patterning, reaction coupling, and biological function. [ABSTRACT FROM AUTHOR]

We present comprehensive numerical results from a study of model H, which describes phase separation kinetics in binary fluid mixtures. We study the pattern dynamics of both density and velocity fields in d = 2, 3. The density length scales show three distinct regimes, in accordance with analytical arguments. The velocity length scale shows a diffusive behavior. We also study the scaling behavior of the morphologies for density and velocity fields and observe dynamical scaling in the relevant correlation functions and structure factors. Finally, we study the effect of quenched random field disorder on spinodal decomposition in model H. [ABSTRACT FROM AUTHOR]

Product service system (PSS) is an effective approach to achieve win–win situation between service providers and consumers, and the design of PSS is the first step of its application. However, on the one hand, PSS is relatively an abstract concept, and what exactly should be considered when designing a PSS still require further exploration; on the other hand, the fast development of information and web technologies bring both opportunities and challenges for PSS design. For example, how to efficiently design the smart & connected products that support remote monitoring and control of service operation, how to build the dynamic service activity flow model that can be intuitively and visually read by human engineers and also can be conveniently deployed on computers, and how to realise edge–cloud collaboration between service providers and consumers. In this regard, a service requirement-oriented four-step generic PSS design method is established, including service mode selection and structured service order generation → smart & connected service product configuration → dynamic event-state knowledge graph-based service activity flow and service resource network configuration → industrial internet-based edge–cloud collaborative service delivering. Finally, a real design case of carbon block grinding and polishing PSS is used for verification. ABBREVIATIONS: AS: assembly service; C: controlling targets or objectives; I: input; M: enabling methods or mechanisms; MRO: maintenance, repair, and operation; MS: maintenance service; O: output; OEE: overall equipment effectiveness; PSS: product service system; PV: processing volume; RxEy-Sz: the relation from Event y to the State z of Service activity x; RxSz-Ey: the relation from the State z of Service activity x to Event y; StateAiCurrent: the current state of Service activity i; StateAiFuturek: the kth possible future state of Service activity i; StateAiHistoryj: the jth historical state of service activity i; StateEy: the state of Event y; Tq: the qth time point in the time line. [ABSTRACT FROM AUTHOR]

The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. D. Sornette [Phys. Rep. 297, 239 (1998)] showed that this behavior can be explained by a discrete scale invariance of the system, which is associated with discrete and equidistant timescales on a logarithmic scale. Examples include such diverse fields as financial crashes, random diffusion, and quantum topological materials. Recent time-resolved experiments and molecular dynamics simulations suggest that discrete scale invariance may also apply to hierarchical dynamics in proteins, where several fast local conformational changes are a prerequisite for a slow global transition to occur. Employing entropy-based timescale analysis and Markov state modeling to a simple one-dimensional hierarchical model and biomolecular simulation data, it is found that hierarchical systems quite generally give rise to logarithmically spaced discrete timescales. By introducing a one-dimensional reaction coordinate that collectively accounts for the hierarchically coupled degrees of freedom, the free energy landscape exhibits a characteristic staircase shape with two metastable end states, which causes the log-periodic time evolution of the system. The period of the log-oscillations reflects the effective roughness of the energy landscape and can, in simple cases, be interpreted in terms of the barriers of the staircase landscape. [ABSTRACT FROM AUTHOR]

To conceptualise biological and mental processes, often a dynamical systems perspective is suggested. In addition to dynamics, the structure of the contextual makeup or world configuration (of an organism or brain) plays a crucial role too, as well as adaptivity of the processes. This paper provides a conceptual perspective where the structure, dynamics, and adaptivity of these processes are distinguished and related to each other via adaptive dynamical systems. Moreover, it is shown how networks can be used to represent this conceptual perspective. Here an adaptive dynamical system of any order of adaptivity can be covered where any level can exert control over the level below. The approach is illustrated by case studies for higher-order adaptive evolutionary processes. One of these case studies shows a fifth-order adaptive dynamical system that models how due to bad environmental influences at a young age, epigenetic effects can lead to a lifelong mental disorder.

Cognitive processes underlie economic relations. In this paper, we develop a conceptual, mathematical, and computational framework for modeling market exchange as a series of dynamically interacting cognitive processes. Specifically, we show how advertisers can build trust and gain confidence in their pricing power to the point that they erode trust and undermine the efficacy of their advertising. Customers conversely orient towards advertisers seeking information or turn away from them as unreliable communicators. These behaviors and the patterns they generate occur inside a state space of unallocated perceived value. They constitute a small subset of the full range of possible strategic and adaptive responses that define cognitive microeconomics.

This review explores the complex relationship between Fear ofFalling (FoF) and Fear of Heights (FoH), and their impact onhuman postural control. FoF encompasses a spectrum of psychologicaland physiological responses that dynamically influencepostural control, while FoH involves perceptual distortionsand heightened physiological arousal in response to elevatedenvironments. Through a comprehensive literature review,we examine the research methods and findings of studieson FoF and FoH. We further propose that Optimal FeedbackControl (OFC) theory is a suitable framework to understandthe computational aspects of how these fears modify posturalcontrol. We aim to provide a nuanced understanding ofFoF and FoH, not only as psychological phenomena but ascomplex, dynamic interactions of cognitive, physiological, andmotor processes influencing an individual's interaction withtheir environment.

As a foundation for social interaction, interpersonal coordination is facilitated by positive social qualities (e.g., cooperation), but undermined in negative contexts (e.g., conflict). Exactly how social factors shape coordination is less clear. Previous literature notes that the way people attend to others impacts how interactions unfold. It is possible therefore, that patterns of social attention also govern coordination. We examined this proposition by using virtual reality to investigate how attentional focus (self vs. other) and partner gaze (direct vs. averted) influence the spontaneous emergence of coordination. The results indicated that: (i) coordination was enhanced in the other (cf. self) focus condition; (ii) coordination was diminished in the averted (cf. direct) gaze condition. These findings suggest that changes in social attention impact interpersonal coordination. More broadly, this work provides further evidence that the emergence of interpersonal coordination fluctuates as a function of social context.

Reservoir computing (RC) offers distinct advantages in extracting spatiotemporal information with low training costs by separating recurrent neural networks into a fixed network with recurrent connections. The quality of the fixed network, known as the reservoir, plays a pivotal role in the performance of the RC system. Our work aims to provide a unified synaptic development framework for RC, constructing a more biologically plausible reservoir to model and understand the neural networks development within the human brain. In this paper, we propose an Autonomous Synaptic Development Reservoir Computing model (ASD-RC) based on an adaptive network of phase oscillators. The reservoir autonomously adjusts the distribution of connection weights in response to external stimuli, forming a task-specific structure. Through experiments and theoretical analyses, we demonstrate that ASD-RC can emulate various synaptic development rules of biological neural networks in \textit{vivo}, including the Hebbian rule and STDP. Furthermore, experiments reveal that combining different development rules can enhance performance on prediction tasks compared to using a single development rule, showcasing the emergence and effects of synergistic development that improve information processing capacity.

Music-making relies on precise temporal control and mutual coordination among performers, particularly to maintain tempo. We evaluate the impact of human-machine interaction and rhythmic subdivisions on tempo change in musical trios. A synchronization-continuation task was performed by trios of human participants interacting with confederates or with algorithmic (i.e. machine) models. Sounded tone onsets were produced by a linear error-correction model, delay-coupled model, and Kuramoto model that replaced a human participant. Inter-onset intervals were examined from participants who performed rhythms in both in-phase and anti-phase conditions while a third group member was either a human or algorithmic model. Trios drifted toward faster tempi more when they contained a human than an algorithmic model. Tempo drift also increased for the aligned rhythms (in-phase) compared to rhythms with rhythmic subdivisions (anti-phase). Finally, the tested algorithmic models replicated the confederate's tempo drift without the use of any period correction mechanisms. This research advances our understanding of unintentional tempo drift, offering insights into ensemble dynamics and models of temporal coordination in groups. Implications for musical coordination and avenues for future research are discussed.

Dyadic social interaction is a complex coordination task involving a large number of interconnected variables. Previous research has shown that metastability -- persistence for an extended, but impermanent, period of time in a non-stable state of a system -- can be a useful lens for understanding what makes an interaction successful. However, this framework has thus far only been applied to para-conversational signals like heart rate and prosody -- not to the semantic content of a conversation. Here, we present pink noise analysis of semantic trajectories as a metric for conversational success and apply this technique to a large open conversation dataset. Our results demonstrate that pink noise in a conversation predicts a host of variables representing participants' perception of conversation quality. These results have implications for optimizing a whole host of difficult dyadic conversations -- like those between political partisans -- and human-computer interactions, with applications for improving large language models' adaptability.

We propose a neural dynamic architecture that models negation processing. The architecture receives a visual scene and a relational phrase like ``The blue object is not to the right of the yellow object'' or ``The blue object is to the right of the green object'' as input, and autonomously determines whether the phrase correctly describes the visual scene. The model is built out of empirically founded components for perceptually grounded cognition and constrained by neural principles. We demonstrate that the model can explain two commonly found reaction time effects: the negation effect in which reaction times are higher for negated than for affirmative phrases, and the polarity-by-truth-value interaction effect in which reaction times for false negated phrases are faster than those for true negated phrases whereas the opposite is true for affirmative phrases. The model is consistent with some aspects of the two-step simulation theory.

Many challenging problems in linguistic analysis concern structures that have a hybrid character---they show evidence of belonging to two, independently motivated types. Proposals often assign them to one or the other class, requiring complication of the theory to handle their exceptionality. We suggest that there is no satisfactory answer to such conundrums under standard, type-based representational theories, for those theories are founded on discrete topologies. As an alternative, we propose “Metric Grammars”--grammatical systems founded on connected topologies. A metric grammar, a recurrent map that has a neural network at its core, changes its grammatical system slightly with each instance of language experience. Focusing on a grammaticalization episode from the history of English---the development of “sort of" and “kind of" from Noun-Preposition structures into adverbs---we provide evidence that metric grammars exhibit statistical anticipation of categorical change, a phenomenon that is difficult to account for with discrete-topology models.

Team coordination is essential for effective performance during critical, stressful events. To better understand processes and states involved at multiple levels of team coordination, we assessed the correspondence between low- and high-level coordination in teams participating in simulation-based medical team training. We computed a measure of low-level team coordination with Multidimensional Recurrence Quantification Analysis, applied to arm movement, heart rate, and skin conductance data. High-level team coordination was captured by annotating video recordings for explicit and implicit, information and action coordination. Three linear mixed-effects model were run, each predicting a type of low-level coordination, based on high-level coordination annotations, accounting for multiple observations per team. Our findings showed that, compared to periods without annotated coordination, explicit- and implicit- information coordination corresponded to significantly different low-level team coordination across each of the studied modalities. Further research is required to assess additional factors related to the temporal variability observed in low-level coordination.

Interpersonal synchrony is a foundation of social interaction. However, as a form of coordination, synchrony is limited to regular, rhythmic actions. As such, research regarding the relationship between synchrony and social factors may not generalise to other forms of interpersonal behaviour. Here, we explored whether factors known to influence synchrony, also impact a complimentary form of coordination, complexity matching. When people interact, complex patterns of variability inherent to their individual behaviour can become more similar (i.e., more coordinated). In pairs, participants completed four walking trials that manipulated social interdependence while their gait patterns were captured. We also measured subclinical levels of social anxiety. Although data collection is ongoing, the results point to social anxiety having a detrimental effect on individual behavioural variability, and in turn, complexity matching. Effects of the interdependence manipulation were also evident, but await further data. These results are discussed with respect to theories of interpersonal dynamics.

Over the last two decades, an increasing number of cognitive scientists have turned to mechanistic explanatory frameworks in their efforts to describe and explain cognitive phenomena. Most mechanistic frameworks conceive of cognitive systems as composed of functionally-individuated components whose functions are narrowly defined by their ranges of possible inputs and outputs, as well as their relations to other components within the phenomenon-producing mechanism. In this paper, I argue that this modular view of cognitive mechanisms as linear systems is not applicable to biological cognitive systems, and offer an alternative characterization using the methodology of Dynamical Systems Theory.

The research focus on adaptivity in complex systems has propelled an exploration of diverse interactions characterized by state transition processes. However, the investigation of functional variances among processes, rooted in fundamental operands, remains insufficient. Recognizing this gap is crucial for unveiling the constituents of state transitions and their functional boundaries during ongoing adaptivity. To address this, our central focus is on quantifying the functional variance in the interactions of fundamental operands. This approach enables a systematic study of complex adaptive networks grounded in the dynamics of cognitive abilities, where elements adapt and evolve based on cognitive processes. To underscore this point, we emphasize translating ontologically irreducible networks into functionally representable ones at the meso-level, which is essential for assessing their effectiveness. Our active investigation during state transitions explores external interventions, aiming to shed light on mutual influences.

We present a novel theory and neural process model of visual selective attention to answer long-standing questions in the field of visual attention. We show that the model with fixed parameter values can explain the unexpected efficiency of triple conjunction search (Nordfang & Wolfe, 2014), the influence of a task-irrelevant size singleton on search (Proulx, 2007), and how a third correlated but task-irrelevant feature improves search efficiency (Found, 1998). It also accounts for critical findings in the attention capture literature without the need to introduce different modes (Bacon & Egeth, 1994), signal-suppression (Gaspelin, Leonard, & Luck, 2015; Gaspelin & Luck, 2018; Lien, Ruthruff, & Hauck, 2021) or an attentional window (Theeuwes, 1992, 2023), shedding new light on recent debates.

Goal-directed behavior requires a dynamic balance between cognitive stability and flexibility. This balance can be modulated by performance-contingent reward. Converging evidence suggests that such rewards promote stability by increasing cue maintenance for response preparation in tasks like the AX continuous performance task. However, task switching studies showed oppositional effects of performance-contingent reward depending on the immediate reward history: Only remaining high reward prospect increases stability, whereas increasing reward prospect increases flexibility. The present study tests whether the flexibility-enhancing effect of increasing reward prospect generalizes beyond task switching scenarios. In a novel cued global-local task, the cue-validity effect served to indicate cognitive flexibility versus stability. Evidence from two experiments shows that increasing reward prospect reduces the cue-validity effects but only in error rates. This suggests more flexibility in terms of increased reactive control compared to remaining high reward prospect, which could be functionally adaptive to prevent extreme stability.

Cognitive development has been hypothesised to be stagelike between the ages of 5-8 years (e.g., Piaget). Yet, cognition varies from moment to moment, in every task, for every child. Studies have demonstrated that cognitive variability is non-trivial, non-random, and meaningful, but attempts for systematic and large-scale longitudinal measurements of cognitive variability have scarcely been undertaken.This project's goal is to create a more detailed empirical record and dynamical account of intra-individual variability in cognitive development of children. We aim to do this with a 3-year longitudinal and multimodal data collection starting at 5 years of age. Half-yearly measurements will be complemented with periods of daily measurements. Our ultimate aim is to build a variability corpus in which we can study variability patterns and developmental transitions, and to connect our findings to “Piaget's new theory”. Our poster will present our methodology and findings from a pilot study.

Self-other integration plays a vital role in efficient synchronization with other humans. Previous research has shown that in simple rhythmic joint action tasks (e.g., tapping), self-other integration can be described using mathematical models of coupled oscillators, representing within- and between-person action-perception links. The present study focuses on investigating self-other behavioral and inter-brain dynamics (dual-EEG) when synchronization is either the goal of the task itself or rather an emergent phenomenon in complex continuous interactions. More specifically, participants produce improvised movements in a ‘mirror-game' paradigm while being explicitly asked to synchronize with the partner (synchronized condition) or produce independent movements with visual feedback of each other (spontaneous condition). Mathematical models of coupled oscillators will be used to reveal emergent dynamics of self-other integration on behavioral and neural level. Moreover, we hypothesize that stronger interpersonal synchronization in the spontaneous condition will lead to stronger sensorimotor alpha and beta desynchronization and higher inter-brain synchronization.

When children solve cognitive problems together, they coordinate their speech, hand movements and head movements. Previous studies with adults have shown that such multimodal coordination is related to better collaboration. We do not know whether this is true for children, however. In this study, dyads of children (6-10 years) discussed and solved balance scale problems together. To investigate children's multimodal coordination, we measured their speech, hand movements and head movements throughout their bouts of discussion, and applied multidimensional Recurrence Quantification Analysis (MdRQA) on these timeseries. We coded the type of collaboration the children engaged in during these bouts of discussion. We measured performance regarding predicting to which side the balance scale would tilt. We will analyse how children's multimodal coordination is related to the type of collaboration and to their performance on the balance scale problems. Our results will show how successful collaboration between children emerges from their multimodal coordination.

Even when early implanted, children with cochlear implants show heterogeneous language skills and often struggle with pragmatic communication aspects. Research aimed at elucidating specific weaknesses at the interactional level has yielded inconsistent findings. We analyse dyadic interactions involving nine hearing-impaired children and fourteen normal-hearing children engaging with an adult during a referential (treasure-hunting) task, periodically alternated with role-reversal sub-tasks (e.g., child-led referential-tasks, child-storytelling). Our investigation employs a multi-level analysis approach, encompassing acoustic features (F0, intensity, speech duration, speech rate), turn-taking dynamics (duration, gaps, overlaps), laughter responsiveness and pragmatic functions, convergence of these features, dialogue acts, contingency, and task success. We compare interactional patterns across groups and conditions. The adoption of a multi-level characterization is grounded in the hypothesis that alignment at "lower levels" serves a functional role and concurrently offers insights into alignment at a conceptual level, thereby facilitating mutual understanding and conversational success, giving insights on underpinning neuro-psychological processes.

How do children bootstrap language through noisy supervision? Most prior works focused on tracking co-occurrences between individual words and referents. We model cross-situational learning (CSL) at sentence level with few (1000) training examples. We compare reservoir computing (RC) and LSTMs on three datasets including complex robotic commands. For most experiments, reservoirs yield superior performance over LSTMs. Surprisingly, reservoirs demonstrate robust generalization when increasing vocabulary size: the error grows slowly. On the contrary, LSTMs are not robust: the number of hidden units needs to be dramatically increased to follow up vocabulary size increase, which is questionable from a biological or cognitive perspective. This suggests that that random projections used in RC helps to bootstrap generalization quickly. To our knowledge, this is a new result in developmental learning modelling. We analyse the evolution of internal representations during training of both recurrent networks and suggest why reservoir generalization seems more efficient.

This paper proposes a maintenance policy for a k-out-of-n: F system operating to fulfil several jobs without interruptions. The system is replaced when the Nth job completes or at the kth failure, whichever occurs first. So, there are some non-failed components when a replacement is done. These components can be sold as second-hand products to continue working in other systems for a while. The price of them is also considered in the proposed maintenance policy. An optimal maintenance policy is studied to minimise long-run average cost under the constraint of relative mean operating time. Comprehensive numerical studies are done to assess the effect of the model parameters on the optimal solutions. Also, to demonstrate the applicability of the proposed plan, a data set related to wind turbine generator failures is considered as a case study. [ABSTRACT FROM AUTHOR]

The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of geometric phase, which is an additional phase factor occurring in dynamical systems, holds the same meaning across different fields of application, its use and interpretation can acquire important nuances specific to the system of interest. In recent years, the development of quantum topological materials and its extension to classical mechanical systems have renewed the interest in the concept of geometric phase. This review revisits the concept of geometric phase and discusses, by means of either established or original results, its critical role in the design and dynamic behaviour of elastic waveguides. Concepts of differential geometry and topology are put forward to provide a theoretical understanding of the geometric phase and its connection to the physical properties of the system. Then, the concept of geometric phase is applied to different types of elastic waveguides to explain how either topologically trivial or non-trivial behaviour can emerge based on the geometric features of the waveguide. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'. [ABSTRACT FROM AUTHOR]

In this article, we deal with finite‐time optimal control of the Euler–Lagrange (E–L) multi‐body mechanism under: uncertain its kinematics and dynamics, displacement blocking of the damaged joint caused by the actuator failure, undesirable forces/torques exerted on the end‐effector and unknown friction forces originating from joints directly driven by the actuators, as well as completely unstructured forces arising from the kinematic singularities appearing on the mechanism trajectory. Based on the suitably defined task space non‐singular terminal sliding manifold and the Lyapunov stability theory, we propose a class of new fault tolerant estimated generalized Jacobian controllers, which seem to be effective in reducing (minimizing) the joint velocity jumps as well as in counteracting the unstructured forces/torques. On account of the fact, that the multi‐body mechanism is a redundant one, a useful criterion function (energy consumption +$$ + $$ manipulability measure) has been utilized in our controller to temporarily optimally track a desired trajectory. The proposed controllers' performance is demonstrated by computer simulations conducted on a redundant manipulator in conditions of unexpected actuator failure and the corresponding joint lock. Additionally, numerical comparisons are also provided with other representative controllers, found in the literature. [ABSTRACT FROM AUTHOR]

In spite of the fact that Roger Barker's groundbreaking research was acclaimed sixty years ago by his contemporaries, it has all been but forgotten among recent generations of psychologists. However, in the wake of developments in dynamical systems and complexity theory, its value for understanding psychological processes in everyday life should be recognized anew. Barker's naturalistic studies of children's daily behaviours in their community revealed that their actions which initially seemed only marginally predictable at the level of individual interaction were, in fact, reliably context-dependent. These results led to the discovery that there are nested structures operating in human habitats as there are throughout the natural world. Barker's discovery of emergent eco-psychological structures, behaviour settings, that are generated from interdependent actions among individuals in the course of everyday life has yet to be fully appreciated because of the continuing dominance of linear, mechanistic models. His recognition of nested systems operating in human habitats is finally coming into its own with the current metatheoretical shift in psychology embracing dynamical models. Additionally, new understanding arises from the consideration of convergent individual developmental histories of situated action and their role in maintaining the historical dimensions of behaviour settings. This article is part of the theme issue 'People, places, things and communities: expanding behaviour settings theory in the twenty-first century'. [ABSTRACT FROM AUTHOR]

In this paper we study the permanence and impermanence for continuous-time competitive Kolmogorov systems via the carrying simplex. We first give an extension to attractors of V. Hutson's results on the existence of repellors in continuous-time dynamical systems that have found wide use in the study of permanence via average Liapunov functions. We then give a general criterion for the stability of the boundary of carrying simplex for competitive Kolmogorov systems of differential equations, which determines the permanence and impermanence of such systems. Based on the criterion, we present a complete classification of the permanence and impermanence in terms of inequalities on parameters for all three-dimensional competitive systems which have linearly determined nullclines. The results are applied to many classical models in population dynamics including the Lotka-Volterra system, Gompertz system, Leslie-Gower system and Ricker system. [ABSTRACT FROM AUTHOR]

The continuous enhancement of optimization algorithms and their parameters has spurred the expansion of AI into novel application domains such as image recognition and smart home technology. This paper employs the system response curve (SRC) to the adaptive learning rate optimizer, addressing challenges associated with the establishment of the optimizer control model and parameter adjustments affecting the dynamic performance of the system. These insights offer theoretical support for the optimizer's application in deep learning models. To begin, the adaptive learning rate optimizer is a time‐varying system. Based on the intrinsic relationship between the network optimization and the control system, the time domain expression and approximate transfer function of the adaptive learning rate optimizer are derived, and the system dynamic model is established. Furthermore, based on the system control model of the optimizer, it is proposed to explain the performance impacts of different optimizers and their hyperparameters on the deep learning model through the SRC. Finally, experiments are performed on the MNIST, CIFAR‐10, UTKinect‐Action3D, and Florence3D‐Action datasets to validate the control theory of explaining optimizers through system response curves. The experimental results show that the recognition performance of the Adaptive Moment Estimate (Adam) is better than that of the Adaptive Gradient (AdaGrad) and Root Mean Square Propagation (RMSprop). Additionally, the learning rate affects the model training speed, and the practical application aligns with the theoretical analysis. [ABSTRACT FROM AUTHOR]

This study presented a novel analytical method to investigate the coupled dynamic behavior of a supercritical helicopter tail transmission system, taking into account the friction-induced self-excitation of the floating spline, the rubbing between the limiting ring device and the shaft, and the time-varying meshing excitation experienced by multiple spiral bevel gear pairs. The tail transmission shaft was first modeled using Timoshenko beam elements in local coordinates. Subsequently, the centralized parameter method was employed to build dynamic models of critical components such as the floating spline, limiting ring devices, and multiple spiral bevel gear pairs. Finally, the system's dynamic equations were derived utilizing the interface coordination principle and spatial coordinate transformation. Numerical analyses were conducted to examine the dynamic behavior of the system, including the coupled vibration properties and the impact laws of the limiting ring device and floating spline on the system's response. The findings indicated that the limiting ring device resulted in a cross-critical vibration reduction in the tail horizontal shaft, achieved through the mechanisms of dry friction and rubbing impact. However, as a consequence, the natural and rubbing frequencies of the other shafts were generated. The self-excited vibration of the system, brought about by the friction of the spline tooth surface, had a significant impact on the shaft that was directly connected. The emergence of the self-excited vibration occurred when the speed surpassed the first-order natural speed of the directly connected shaft, with the corresponding self-excited frequency being the first-order natural frequency of said shaft. With the increase in the tooth surface friction coefficient of the spline, it even caused continuous rubbing between the shaft and the limiting ring device under a supercritical condition. The proposed dynamic analysis approach holds promise in offering theoretical guidance for the reduction of vibration and noise generated in supercritical tail transmission systems. [ABSTRACT FROM AUTHOR]

In the current work, we study the eigenvalue distribution results of a class of non-normal matrix-sequences which may be viewed as a low rank perturbation, depending on a parameter β > 1 , of the basic Toeplitz matrix-sequence { T n (e i θ) } n ∈ N , i 2 = − 1. The latter of which has obviously all eigenvalues equal to zero for any matrix order n , while for the matrix-sequence under consideration we will show a strong clustering on the complex unit circle. A detailed discussion on the outliers is also provided. The problem appears mathematically innocent, but it is indeed quite challenging since all the classical machinery for deducing the eigenvalue clustering does not cover the considered case. In the derivations, we resort to a trick used for the spectral analysis of the Google matrix plus several tools from complex analysis. We only mention that the problem is not an academic curiosity and in fact stems from problems in dynamical systems and number theory. Additionally, we also provide numerical experiments in high precision, a distribution analysis in the Weyl sense concerning both eigenvalues and singular values is given, and more results are sketched for the limit case of β = 1. [ABSTRACT FROM AUTHOR]

In this article, anti‐unwinding sliding mode attitude maneuver control with predefined time is investigated for rigid spacecraft with input saturation. First, a nonsingular sliding function containing two equilibrium points is designed to ensure the predefined‐time convergence of system states and unwinding‐free performance of the closed‐loop system on the sliding phase. Then, an auxiliary system with a dynamic parameter is presented to compensate the impact of input saturation. With this parameter, the auxiliary system can handle input saturation that occurs. Based on the sliding function and the auxiliary system, an attitude maneuver controller is developed to guarantee the robustness of the closed‐loop system to bounded external disturbance. Under the designed controller, the states of the closed‐loop system are driven into a neighborhood of the sliding surface within a predefined time. Moreover, the unwinding phenomenon is also avoided on the reaching phase. Numerical simulation results illustrate the unwinding‐free performance and predefined‐time convergence of the closed‐loop system under the proposed control strategy. [ABSTRACT FROM AUTHOR]

This article explores the criteria for fixed‐time stability (FxTS) within nonlinear impulsive dynamical systems, encompassing both stabilizing and destabilizing impulses. Initially, employing the Lyapunov method, the article delineates a criterion for FxTS, particularly when impulsive sequences are delineated by an average impulsive interval. Following this, the article innovatively applies two integral inequalities to introduce an optimized criterion for uniform impulsive sequences, evidencing its lesser conservativeness relative to the initial criterion. Moreover, this article derives a necessary condition for dynamical systems subjected to destabilizing impulses. Intriguingly, the investigation reveals the existence of a minimal threshold for the maximum impulsive interval, below which the system cannot achieve FxTS. This result elucidates why existing literature uniformly imposes a specific condition on the impulsive interval for destabilizing impulses. Finally, the efficacy of the proposed theory is underscored through numerical examples. [ABSTRACT FROM AUTHOR]

When a mechanical backlash between the loading piston rod and the steering gear piston rod connection of the electro‐hydraulic load simulator (EHLS), it will lead to poor loading accuracy. To solve this problem, an adaptive backstepping sliding mode controller based on the backlash feedforward compensation and state observer is proposed. First, the mechanism of surplus force generation in the EHLS is analyzed, and a mathematical model containing position disturbance and backlash nonlinearity is established based on the analysis results. Second, a state observer is designed to estimate the system state and the parameter adaptive law is designed to estimate the system parameters. Third, the adaptive backstepping method is combined with the non‐singular terminal sliding mode control (NTSMC) strategy to deal with the position disturbance and parameter uncertainty and to enhance the system's dynamic performance. Finally, a backlash feed‐forward compensator is engineered to restrain the detrimental effects caused by the backlash nonlinearity, and the simulation experimental results show that the designed new method can realize the precise loading of the EHLS under different working conditions, and the surplus force is suppressed better at the same time. [ABSTRACT FROM AUTHOR]

In this article, we argue that social systems with fission–fusion (FF) dynamics are best characterized within a complex adaptive systems (CAS) framework. We discuss how different endogenous and exogenous factors drive scale-dependent network properties across temporal, spatial and social domains. Importantly, this view treats the dynamics themselves as objects of study, rather than variously defined notions of static 'social groups' that have hitherto dominated thinking in behavioural ecology. CAS approaches allow us to interrogate FF dynamics in taxa that do not conform to more traditional conceptualizations of sociality and encourage us to pose new types of questions regarding the sources of stability and change in social systems, distinguishing regular variations from those that would lead to system-level reorganization. This article is part of the theme issue 'Connected interactions: enriching food web research by spatial and social interactions'. [ABSTRACT FROM AUTHOR]

Digital twin represents the core technology to realize the dynamic monitoring of complex industrial systems. However, the human body, as the most complex system in the physical world, digital twin is rarely applied in it. In this study, we successfully demonstrated a digital twin in the human biomedical application by proposing a dynamic monitoring system of the upper limb force. In this system, the real upper limb drives the motion of the virtual one in real-time and dynamically updates the force. Meanwhile, the virtual upper limb feeds back the monitoring-results of the force to the controller of the real upper limb via immersive virtual reality interaction. Experimental results of the typical motions of the upper limb revealed that the proposed system functioned interactively in real-time in a non-invasive manner, while ensuring the accurate solving of the muscle force. In conclusion, our digital twin-driven system is of great importance for rehabilitation medicine, biomechanical scientific research and physical training, promoting the application of the digital twin in the human biomedical field. [ABSTRACT FROM AUTHOR]

Repulsion systems under the discrete dynamical systems perspective are considered. The goal is to study the nonlinear dynamics of an arrangement of individual or cells under various types of repulsion laws. Repulsion is a natural mechanism, so we consider the following laws: global, open, cyclic and bounded repulsion. A first scenario under consideration is when particles are freely located on an Euclidean space and the second scenario where they are restricted to remain in a bounded set. We consider those two scenarios under the previous types of repulsion. The analysis culminates in a unification of two mechanisms: attraction and repulsion via a specific social behaviour problem. [ABSTRACT FROM AUTHOR]

• Extended Goodwin model integrates endogenous technological change and labor supply. • Reinterpretation of induced innovation in terms of mechanization. • Application of 3D-Hopf bifurcation theorem reveals limit cycle dynamics. • Employment rate's effect on productivity as a bifurcation parameter defines cycle stability. • Numerical simulation for 10 OECD economies and sensitivity analysis. This paper extends the Goodwin model of distributive cycles by incorporating the simultaneous endogeneity of technical change and labor supply within a classical-Marxian framework. It reinterprets induced innovation, suggesting that firms optimize mechanization to maximize cost reduction, obtaining a micro-founded relationship between mechanization and the wage share. Additionally, it assumes a positive relationship between labor supply and the employment rate. The resulting three-dimensional dynamical system includes wage share, employment rate, and capital-output ratio as state variables. The Hopf bifurcation theorem reveals the emergence of limit cycles as the employment rate's effect on labor productivity (reserve-army-creation effect) approximates a critical value from below. Numerical simulations for 10 OECD countries illustrate the cyclical nature of the model and its consistency with empirical patterns. Furthermore, a sensitivity analysis explores the effect of parameters variations, emphasizing the social dimensions of productivity and labor supply as critical factors defining the stability of distributive cycles. [ABSTRACT FROM AUTHOR]

The Goodwin–Keen model was introduced to study the structural instability of debt-financed economies. Despite its theoretical appeal, no empirical study has focused on this model to date. Using u.s. data for non-financial firms over the period 1959–2019, this paper tests the empirical validity of a Goodwin–Keen model accounting for dividends. We propose a two-step procedure to simultaneously estimate parameters and quantify their uncertainty. The model satisfactorily captures the historical cycles in the wage share and employment rate, while reflecting the trend growth in the debt-to-output ratio. The estimation provides meaningful parameters, although their large uncertainty suggests that the model fails to fully account for the private debt dynamics. The estimated model assigns a probability of at most 11% to the occurrence of a private-debt overhang over the 21st century. However, it would have failed to foretell the Global Financial Crisis. Further work is therefore needed to improve its prospective capacity. • A new estimation strategy is used to estimate the parameters of a Goodwin–Keen model for the United-States (1959-2019). • The model captures the historical wage-share, employment rate and corporate debt-to-output ratio trajectories. • The model's behavior is discussed based on prospective simulations and a backtesting over the 2008 crisis period. [ABSTRACT FROM AUTHOR]

The consolidation of Building Information Modelling (BIM) on construction sites and the preparation of the Internet-of-Things (IoT) in urban city planning are on-going processes. Therefore, the operation of modern total stations in dynamic urban scenarios becomes inevitable and often reveals the limitations of state-of-the-art approaches. This paper discusses augmentation strategies for the automatic operation of total stations. Additional internal sensor information and external facility information can be used to increase the resilience of the systems and enable them to adapt to changing circumstances. This is demonstrated by the examples of a changing prism orientation due to vandalism, local refraction effects due to air-conditioning and dynamic obstructions due to traffic. [ABSTRACT FROM AUTHOR]

Let π: (X, T) → (Y, S) be a factor map between two topological dynamical systems, and F a Furstenberg family of ℤ. We introduce the notion of relative broken F -sensitivity. Let F s (resp. F pubd , F inf ) be the families consisting of all syndetic subsets (resp. positive upper Banach density subsets, infinite subsets). We show that for a factor map π: (X, T) → (Y, S) between transitive systems, π is relatively broken F -sensitive for F = F s or F pubd if and only if there exists a relative sensitive pair which is an F -recurrent point of (Rπ, T(2)); is relatively broken F inf -sensitive if and only if there exists a relative sensitive pair which is not asymptotic. For a factor map π: (X, T) → (Y, S) between minimal systems, we get the structure of relative broken F -sensitivity by the factor map to its maximal equicontinuous factor. [ABSTRACT FROM AUTHOR]

We continue our study on the global dynamics of a non- local reaction-diffusion-advection system modeling the population dynamics of two competing phytoplankton species in a eutrophic environment, where the species depend solely on light for their metabolism. In our previous works, we proved that system (1.1) is a strongly monotone dynamical system with respect to a non-standard cone, and some competitive exclusion results were obtained. In this paper, we aim to demonstrate the existence of coexistence steady state as well as competitive exclusion. Our results highlight that advection in dispersal strategy can lead to transitions between various competitive outcomes. [ABSTRACT FROM AUTHOR]

Climate change is impacting marine species, leading to shifts in their distribution to higher latitudes and to deeper locations. Parasite communities are dynamic systems influenced by biotic and abiotic factors, making them valuable tools for studying ecological processes of their hosts. This work aims to assess possible changes in parasite structure that occurred in the northern stock of Cynoscion guatucupa in the Argentine Sea, over approximately 25 years, by using parasites as tags in a region characterized as a hotspot of significant warming in recent decades. Parasite assemblages of adult and juvenile fish from two periods caught at two regions of the Argentine Sea were analyzed. Species richness remained relatively constant across samples, although four of the eight compared species from juvenile fish showed significant increases in prevalence, while for adults three species decreased. Differences in parasite assemblages were significant between periods, but not between regions, indicating that the stock structure has apparently remained stable in recent years, even under a warming process that, in turn, seems to have affected its parasite assemblages which however, continue showing homogeneous parasitological attributes throughout the habitats. Most results indicate that changes in parasite burdens are not related to the population density or geographic distribution of C. guatucupa, but to changes in temperature, salinity or in the density of top predators. Parasites seem to have felt the impact of global change before their host, thus, they can be considered early sentinels to monitor the stability and distribution of this important resource. [ABSTRACT FROM AUTHOR]

Stochastic bifurcation of dynamical system induced by Lévy noise is investigated in this paper from the global viewpoint, which is demonstrated based on the global attractor obtained with the compatible cell mapping (CCM) method. Compared with the traditional cell mapping method, the efficiency of CCM method is greatly improved by concentrating the computational domain on the covering set of the global attractor rather than the whole state space. The computation time can be further reduced by a simple parallel procedure with the block matrix strategy. With the proposed method, the evolutionary process of global properties has been presented. It shows that the shape and size of stochastic attractors and stochastic saddles vary along the direction of unstable manifold with the parameters of Lévy noise. Stochastic bifurcation occurs when stochastic attractor collides with stochastic saddle. It can be also found that the global bifurcation under Lévy noise is discontinuous because of the jump property. The results are significantly different from those of Gaussian noise, which reveals a distinct global evolutionary mechanism of stochastic bifurcation. Furthermore, it also indicates that the CCM method with block matrix is an effective tool for global analysis. [ABSTRACT FROM AUTHOR]

Fibrous dysplasia (FD) is a mosaic non-inheritable genetic disorder of the skeleton in which normal bone is replaced by structurally unsound fibro-osseous tissue. There is no curative treatment for FD, partly because its pathophysiology is not yet fully known. We present a simple mathematical model of the disease incorporating its basic known biology, to gain insight on the dynamics of the involved bone-cell populations, and shed light on its pathophysiology. We develop an analytical study of the model and study its basic properties. The existence and stability of steady states are studied, an analysis of sensitivity on the model parameters is done, and different numerical simulations provide findings in agreement with the analytical results. We discuss the model dynamics match with known facts on the disease, and how some open questions could be addressed using the model. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the topological entropy of shrinking target problem in nonautonomous dynamical systems (NDSs). After providing the shrinking target problem of the topological version in NDSs, we obtain a general formula for computing the topological entropy of it. More precisely, we show that the entropy distribution principle still holds in NDSs and apply it to estimate the lower bound of the formula. In addition to the specification property, the concept of control non-decreasing property about the Bowen metric proposed by us is taken as a supplementary condition. Furthermore, we get the connection about the topological entropy between the shrinking target problem and the whole system. This extends the result of Ma et al. [Discrete Contin. Dyn. Syst. 39(5) (2019), pp. 2455–2471], corresponding to the case when the maps are the same as the more general case of different maps. [ABSTRACT FROM AUTHOR]