Attractor States Research Articles

Attractor States in Second Language Development

Identifying changing patterns of stability and variability is crucial when examining second language development (SLD) from a complex dynamic systems theory (CDST) perspective (Larsen-Freeman, 2020). By studying attractor states, or recurrent patterns of stability, light can be shed on the underlying dynamics of a complex dynamic system (van Geert & Verspoor, 2015). In the context of SLD, attractor states can be observed in individuals’ linguistic behaviors, as well as learners’ interactions with others (Hiver, 2014; van Geert & Verspoor, 2015). As such, attractor states have been cited in recent SLD literature (e.g., Amerstorfer, 2020; Evans & Larsen-Freeman, 2020; Syed et al., 2021; Gillies & Roger, 2022). The conceptual unpacking of attractor states can therefore be invaluable for SLD scholars seeking to enter the realm of CDST. Accordingly, serving as a stepping stone for those looking to foray into the CDST paradigm, this forum piece offers a definition of attractor state, identifies and describes different types of attractor states, clarifies some possible misconceptions about attractor states, and provides a few examples of attractor states in SLD.

Social Search and Resource Clustering as Emergent Stable States.

Social search has stably evolved across various species and is often used by humans to search for resources (such as food, information, social partners). In turn, these resources frequently come distributed in patches or clusters. In the current work, we use an ecologically inspired agent-based model to investigate whether social search and clustering are stable outcomes of the dynamical mutual interactions between the two. While previous research has studied unidirectional influences of social search on resource clustering and vice versa, the current work investigates the consequential patterns emerging from their two-way interactions over time. In our model, consumers evolved search strategies (ranging from competitive to social) as adaptations to their environmental resource structures, and resources varied in distributions (ranging from random to clustered) that were shaped by agents' consumption patterns. Across four experiments, we systematically analyzed the patterns of influence that search strategies and environment structure have on each other to identify stable attractor states of both. In Experiment 1, we fixed resource clustering at various levels and observed its influence on social search, and in Experiment 2, we observed the influence of social search on resource distribution. In both these experiments we found that increasing levels of one variable produced increases in the other; however, at very high levels of the manipulated variable, the dependent variable tended to fall. Finally in Experiments 3 and 4, we studied the dynamics that arose when resource clustering and social search could both change and mutually influence each other, finding that low levels of social search and clustering were stable attractor states. Our simple 2D model yielded results that qualitatively resemble those across a wide range of search domains (from physical search for food to abstract search for information), highlighting some stable outcomes of mutually interacting consumer/resource systems.

Chaotic mixing properties under rotation plus revolution revealed by purification experiments and numerical simulations

BackgroundThe purification process of Zn-containing solid waste causes severe pollution, and energy and material consumption because of its low mechanical stirring efficiency. Thus, a new effective stirring method called rotation plus revolution (RPR) has been proposed. MethodsThe enhanced mixing performance of eccentric rotation (ER), orbital rotation (OR), and RPR were investigated through purification experiments and numerical simulations. Combined with chaotic mixing theory, the influence of momentum transfer on the reaction rate controlled by diffusion is analyzed. Significant findingsCompared with ER and OR, RPR induces a specific chaotic attractor state in the fluid, which destabilizes the flow field, thereby realizing chaotic mixing and destroying the isolated mixing region. RPR promotes sufficient momentum diffusion, and the trajectory of folding and stretching increases the effective collision probability per unit time, greatly improving the reaction rate. At 60 min, the purification rate of RPR reached 96.9%, which was 37.8 and 35.1% higher than those of ER and OR, respectively. RPR also had a higher energy utilization rate, and its unit ion purification energy decreased by 2.3% and 20.4% compared with ER and OR, respectively. Overall, RPR improved the purification efficiency with low energy consumption, thereby saving energy and reducing emissions.

Robust and brain-like working memory through short-term synaptic plasticity.

Working memory has long been thought to arise from sustained spiking/attractor dynamics. However, recent work has suggested that short-term synaptic plasticity (STSP) may help maintain attractor states over gaps in time with little or no spiking. To determine if STSP endows additional functional advantages, we trained artificial recurrent neural networks (RNNs) with and without STSP to perform an object working memory task. We found that RNNs with and without STSP were able to maintain memories despite distractors presented in the middle of the memory delay. However, RNNs with STSP showed activity that was similar to that seen in the cortex of a non-human primate (NHP) performing the same task. By contrast, RNNs without STSP showed activity that was less brain-like. Further, RNNs with STSP were more robust to network degradation than RNNs without STSP. These results show that STSP can not only help maintain working memories, it also makes neural networks more robust and brain-like.

Analytical studies on complete, lag and anticipation synchronization in cascaded circuits with numerical and experimental confirmation

We report in this paper, the explicit analytical solutions developed for studying the different types of synchronization behaviors such as complete, lag and anticipation synchronization observed in cascaded circuits without any delay factors in the system. The Pecora–Carroll method of synchronization of unidirectionally coupled systems, which has not been earlier studied through explicit analytical solutions is reported in this paper. The emergence of different synchronization phenomena and the nature of evolution of the synchronization behavior has been discussed. Further, it has also been confirmed that the evolution of anticipation from lag through complete synchronization along with the attenuation, amplification of the subsystem signal occurs as a generalized phenomenon irrespective of the nature of the chaotic attractor state of the drive and the system parameters. The Hamilton energy of the cascaded system for different types of synchronization is reported. The numerical simulation and electronic circuit experimental results are presented to confirm the analytical results.

Studying Mental Health Problems as Systems, Not Syndromes

Despite decades of clinical, sociopolitical, and research efforts, progress in understanding and treating mental health problems remains disappointing. I discuss two barriers that have contributed to a problematic oversimplification of mental illness. The first is diagnostic literalism, mistaking mental health problems (complex within-person processes) for the diagnoses by which they are classified (clinically useful idealizations to facilitate treatment selection and prognosis). The second is reductionism, the isolated study of individual elements of mental disorders. I propose conceptualizing people’s mental health states as outcomes emerging from complex systems of biological, psychological, and social elements and show that this systems perspective explains many robust phenomena, including variability within diagnoses, comorbidity among diagnoses, and transdiagnostic risk factors. It helps us understand diagnoses and reductionism as useful epistemological tools for describing the world, rather than ontological convictions about how the world is. It provides new lenses through which to study mental illness (e.g., attractor states, phase transitions), and new levers to treat them (e.g., early warning signals, novel treatment targets). Embracing the complexity of mental health problems requires opening our ivory towers to theories and methods from other fields with rich traditions, including network and systems sciences.

Versifying adversity: Using dramaturgically framed poetic inquiry to explore complexity in the second language learning experience

Over the past 15 years, research in the field of second language learning motivation has been dominated by the second language (L2) motivational self system, conceptualizing motivation as a combination of the ideal L2 self, ought-to L2 self, and L2 learning experience. Despite the analytical strength demonstrated by the self components of the L2 motivational self system, the influential role of the L2 learning experience component is still in need of greater elucidation. Using a hybridized research approach combining a complex dynamic systems (CDS) perspective with dramaturgical coding and poetic inquiry, we unpack a Japanese undergraduate student's L2 learning experience. Taking the learner as both a complex system and a situated actor, key themes are identified and explored as attractor states. Humanizing what can often be an impersonal perspective, dramaturgically framed poetic inquiry is seen to add analytical power to the CDS perspective and afford its artistic and evocative representation.

Bursting dynamics and the bifurcation mechanism of a modified Rayleigh-van der Pol-Duffing oscillator

In this paper, complex bursting patterns in a modified Rayleigh-van der Pol-Duffing oscillator(abbreviated as MRPDO) under the simultaneous effect of parametric and external excitations are given theoretically by fast-slow analysis method. Four different kinds of bursting oscillations, i.e. bursting of compound asymmetric ‘Homoclinic/Homoclinic’ type, bursting of compound asymmetric ‘delayed Homoclinic/Homoclinic’ type, bursting of compound ‘fold/delayed Homoclinic connection/supHopf-supHopf/supHopf’ type and bursting of ‘fold/delayed Homoclinic’ type, are studied. For bursting of compound ‘fold/delayed Homoclinic connection/supHopf-supHopf/supHopf’ type, we explain the delay generation mechanism. Based on the characteristics of the Homoclinic-limit cycles, we propose the concepts of the approximate quiescent state and peculiar limit cycle attractor.

Reproducing size distributions of swarms of barchan dunes on Mars and Earth using a mean-field model

We apply a mean-field model of interactions between migrating barchan dunes, the CAFE model, which includes spontaneous calving, aggregation, fragmentation, and mass-exchange, yielding a steady-state size distribution that can be resolved for different choices of interaction parameters. The CAFE model is applied to empirically measured distributions of dune sizes in two barchan swarms in the north circumpolar region of Mars, three swarms in Morocco, and one in Mauritania, each containing more than 1000 bedforms. When the sizes of bedforms are rescaled by the mean size in each zone two attractor states appear, with the Tarfaya zones all displaying a common distribution and the Martian and Mauritanian zones sharing a different distribution. Comparison of these attractor states with the outputs of the CAFE model reveals that the Tarfaya-type distribution results from a preference for aggregation and fragmentation interactions whereas the Mars–Mauritania distribution is more likely a result of exchange–dominated interactions. We observe that there appears to be a greater number of collisions happening in Tarfaya than in the other areas which is consistent with a greater rate of aggregation–fragmentation processes as suggested by our model. Our comparison with the CAFE model also predicts a universal rule for the outputs of the different types of interactions with exchange interactions favouring the production of two dunes roughly equal in size. Fragmentation interactions often result in three bedforms with volumes approximately in the ratio 1:1:2. Finally, we find that spontaneous calving of dunes does not play an important role in shaping the size distributions in barchan swarms.

Revisiting transient coarsening kinetics: a new framework in the Lifshitz-Slyozov-Wagner space

Phase coarsening in multiphase materials is a fundamental and crucial process in the study of microstructure evolution, for which a thorough understanding of kinetics can make a significant contribution to material processing and performance design. In this work, a new framework in the dimensionless Lifshitz-Slyozov-Wagner space is developed to study the kinetics of transient coarsening co-controlled by interface and matrix diffusion. The dynamic equations for individual particles are derived from the thermodynamic extremal principle, in consideration of energy dissipations by matrix diffusion, interface migration/reaction, and trans-interface diffusion. The effects of initial particle size distribution and finite volume fractions are clarified. Different from the conventional viewpoints, the time for transient coarsening is found to change non-monotonically with the width and tail length of the initial distribution. The ultralong transient coarsening with ‘quasi-steady’ distributions can occur for systems initiated from both the ‘wide & long tail’ and ‘narrow & short tail’ distributions. Furthermore, this work proves the existence of a unique attractor state for the steady stage and reveals the numerical origin of ‘quasi-steady’ distributions, which answers Brown's unsolved puzzle for years [LC Brown. Acta Metall 1989;37:71]. Finally, an increase in volume fraction is shown to directly shorten the transient stage dominated by single mechanism (matrix diffusion or interface), but indirectly delay the transition from the interface-dominated state to the diffusion-controlled stage. These findings not only offer new insights into the previous observations in microgravity experiments [VA Snyder, J Alkemper, PW Voorhees, Acta Mater 2001;23:699], but also theoretically describe the limiting coarsening behaviors at ultrahigh volume fractions [H Yan, KG Wang, ME Glicksman. Acta Mater 2022;117964].

An attractor domain model of seasonal and inter‐annual β diversity of stream macroinvertebrate communities

Abstract Ecological communities are dynamic systems that vary within and across years. In streams, disturbance by spates and the emergence of adult insects during the rainy summer contrast with more stable conditions in the dry winter and can potentially generate distinct and repeatable community states across years. However, demographic stochasticity and the legacies of previous spates may hamper the full attainment of characteristic community states associated with seasons. We developed an attractor domain model encapsulating these factors and hypothesised: (1) partially distinct rainy (summer) and dry (winter) communities. High benthic dynamism during the rainy period should cause higher inter‐annual variability, leading to (2) higher temporal β diversity among rainy periods than among dry periods. Historical effects (e.g., demographic stochasticity and disturbance by spates) should accumulate over the years and lead to (3) increased variation in community structures sampled further apart in time; furthermore, (4) this increase in variation should be higher among rainy than among dry communities. We used data of stream macroinvertebrates (mostly insects) in a subtropical basin in Brazil to evaluate inter‐annual variation using rank‐concordance statistics of the most common species and dissimilarity using all species. For each stream site, samples obtained in the two seasons tended to show distinct community structure using relative abundance data but were much less distinct using species composition (presence–absence). Temporal β diversity was higher among rainy than among dry seasons. The β diversity of both seasons increased with time, although this increase was 2–3 times greater during the rainy season. Our results support a model in which rainy (summer) communities are disrupted by the high dynamism caused by spates and the emergence of adult insects. The low intensity of these two factors during dry (winter) periods allows local environmental conditions to drive community structures toward a less variable, recurrent attractor state. However, the increase in β diversity with time indicates that the legacy effects of previous disturbances and demographic stochasticity preclude the full attainment of a definite stable state and that only a domain of states is approached.

A dynamic approach to understanding motivation in an interpreting course

Guided by a dynamic systems theory framework, this study observed and investigated how the motivation of students learning interpreting changed during an undergraduate English-Chinese interpreting course, with the aim of delineating, if any, typical trajectories. Nine students submitted anonymous reflective learning logs five times to yield qualitative data; one of the nine participated in an in-depth interview. All the data were coded and analysed on the basis of grounded theory. The findings revealed the intra- and inter-individual variability in terms of motivational dynamics, which constantly evolved and interacted with a variety of factors. For these students, high motivation in the initial conditions did not guarantee stable performance later. Throughout the study, the students self-organised into different attractor states under the influence of various internal and external elements. For them, an encouraging teacher led to increased motivation, whereas deeply ingrained diffidence eroded it. Two swing factors, which refer to factors that either strengthen or weaken motivation, were mid-term exams and practice. Furthermore, an archetype of a strongly motivated student was identified and discussed at length, thereby adding another piece of jigsaw to the broader picture of motivational dynamics in second language acquisition. The conclusions drawn from the present study are expected to enhance the understanding of teachers and researchers about the intricate nature of language-learning motivation, especially for interpreting learning, and the encompassing potential embedded in dynamic systems theory.

From Adaptive Locomotion to Predictive Action Selection – Cognitive Control for a Six-Legged Walker

Locomotion in animals provides a model for adaptive behavior as it is able to deal with various kinds of perturbations. Work in insects suggests that this evolved flexibility results from a modular architecture, which can be characterized by a recurrent neural network allowing for various emerging attractor states. Whereas a lower control-level coordinates joint movements on a short timescale, a higher-level handles action selection on longer timescales. Implementation of such a control system on a walking hexapod robot was able to deal with various walking patterns including disturbances such as uneven terrain or loss of a leg. Here, we propose a cognitive expansion to the adaptive control system that allows dealing with novel challenging situations. This approach makes use of an internal simulation-based planner that is triggered when the model-free controller fails to recover from an unstable pose. Using a grounded internal body model, the planner then tries, in internal simulation, different solutions out of context, and thus, proposes a new plan to be executed on the real robot. We demonstrate the feasibility of this control approach for walking over terrain with uncertain footholds in three scenarios.

Core motifs predict dynamic attractors in combinatorial threshold-linear networks.

Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of nonlinear dynamics including multistability, limit cycles, quasiperiodic attractors, and chaos. In prior work, we have developed a detailed mathematical theory relating stable and unstable fixed points of CTLNs to graph-theoretic properties of the underlying network. Here we find that a special type of fixed points, corresponding to core motifs, are predictive of both static and dynamic attractors. Moreover, the attractors can be found by choosing initial conditions that are small perturbations of these fixed points. This motivates us to hypothesize that dynamic attractors of a network correspond to unstable fixed points supported on core motifs. We tested this hypothesis on a large family of directed graphs of size n = 5, and found remarkable agreement. Furthermore, we discovered that core motifs with similar embeddings give rise to nearly identical attractors. This allowed us to classify attractors based on structurally-defined graph families. Our results suggest that graphical properties of the connectivity can be used to predict a network's complex repertoire of nonlinear dynamics.

Mechanisms of distributed working memory in a large-scale network of macaque neocortex.

Neural activity underlying working memory is not a local phenomenon but distributed across multiple brain regions. To elucidate the circuit mechanism of such distributed activity, we developed an anatomically constrained computational model of large-scale macaque cortex. We found that mnemonic internal states may emerge from inter-areal reverberation, even in a regime where none of the isolated areas is capable of generating self-sustained activity. The mnemonic activity pattern along the cortical hierarchy indicates a transition in space, separating areas engaged in working memory and those which do not. A host of spatially distinct attractor states is found, potentially subserving various internal processes. The model yields testable predictions, including the idea of counterstream inhibitory bias, the role of prefrontal areas in controlling distributed attractors, and the resilience of distributed activity to lesions or inactivation. This work provides a theoretical framework for identifying large-scale brain mechanisms and computational principles of distributed cognitive processes.

Universal attractors in language evolution provide evidence for the kinds of efficiency pressures involved

Efficiency is central to understanding the communicative and cognitive underpinnings of language. However, efficiency management is a complex mechanism in which different efficiency effects—such as articulatory, processing and planning ease, mental accessibility, and informativity, online and offline efficiency effects—conspire to yield the coding of linguistic signs. While we do not yet exactly understand the interactional mechanism of these different effects, we argue that universal attractors are an important component of any dynamic theory of efficiency that would be aimed at predicting efficiency effects across languages. Attractors are defined as universal states around which language evolution revolves. Methodologically, we approach efficiency from a cross-linguistic perspective on the basis of a world-wide sample of 383 languages from 53 families, balancing all six macro-areas (Eurasia, North and South America, Australia, Africa, and Oceania). We explore the grammatical domain of verbal person–number subject indexes. We claim that there is an attractor state in this domain to which languages tend to develop and tend not to leave if they happen to comply with the attractor in their earlier stages of evolution. The attractor is characterized by different lengths for each person and number combination, structured along Zipf’s predictions. Moreover, the attractor strongly prefers non-compositional, cumulative coding of person and number. On the basis of these and other properties of the attractor, we conclude that there are two domains in which efficiency pressures are most powerful: strive towards less processing and articulatory effort. The latter, however, is overridden by constant information flow. Strive towards lower lexicon complexity and memory costs are weaker efficiency pressures for this grammatical category due to its order of frequency.

Homeostatic control of synaptic rewiring in recurrent networks induces the formation of stable memory engrams.

Brain networks store new memories using functional and structural synaptic plasticity. Memory formation is generally attributed to Hebbian plasticity, while homeostatic plasticity is thought to have an ancillary role in stabilizing network dynamics. Here we report that homeostatic plasticity alone can also lead to the formation of stable memories. We analyze this phenomenon using a new theory of network remodeling, combined with numerical simulations of recurrent spiking neural networks that exhibit structural plasticity based on firing rate homeostasis. These networks are able to store repeatedly presented patterns and recall them upon the presentation of incomplete cues. Storage is fast, governed by the homeostatic drift. In contrast, forgetting is slow, driven by a diffusion process. Joint stimulation of neurons induces the growth of associative connections between them, leading to the formation of memory engrams. These memories are stored in a distributed fashion throughout connectivity matrix, and individual synaptic connections have only a small influence. Although memory-specific connections are increased in number, the total number of inputs and outputs of neurons undergo only small changes during stimulation. We find that homeostatic structural plasticity induces a specific type of “silent memories”, different from conventional attractor states.

Adaptive mutation quantum-inspired squirrel search algorithm for global optimization problems

This paper presents a novel Adaptive Mutation Quantum-inspired Squirrel Search Algorithm (AM-QSSA). Firstly, based on the population mutation, a location-update of quantum state correlative and attractor method is proposed. By introducing a random process to modify the sliding factor of the local attractor, the inevitable lack of diversity in the population renewal method is solved. The premature convergence problem of adaptive mutation rate improvement algorithm based on squirrel position update mode is introduced. Meanwhile, the paper decomposes the location update process of the SSA, and improves it with quantum-behavior. Furthermore, it proposes a novel quantum-inspired squirrels search algorithm. This method finds the complementary effect between quantum behavior and squirrel search algorithm, and solves the problem of premature convergence probability of SSA. In addition, it improves population diversity, and achieves the balance between global and local search. The efficiency of the proposed AM-QSSA is evaluated using exploitation analysis, exploration analysis, success rate analysis, convergence rate analysis on classical benchmark functions as well as Congress on Evolutionary Computation (CEC) 2017 test functions. For further study, AM-QSSA optimizes an image registration problem for an extensive study to check its applicability. The results reveal that AM-QSSA is more efficient and stable than SSA. And it is comparable to the most advanced optimization algorithms.

Entorhinal-hippocampal interactions lead to globally coherent representations of space.

The firing maps of grid cells in the entorhinal cortex are thought to provide an efficient metric system capable of supporting spatial inference in all environments. However, whether spatial representations of grid cells are determined by local environment cues or are organized into globally coherent patterns remains undetermined. We propose a navigation model containing a path integration system in the entorhinal cortex and a cognitive map system in the hippocampus. In the path integration system, grid cell network and head direction (HD) cell network integrate movement and visual information, and form attractor states to represent the positions and head directions of the animal. In the cognitive map system, a topological map is constructed capturing the attractor states of the path integration system as nodes and the transitions between attractor states as links. On loop closure, when the animal revisits a familiar place, the topological map is calibrated to minimize odometry errors. The change of the topological map is mapped back to the path integration system, to correct the states of the grid cells and the HD cells. The proposed model was tested on iRat, a rat-like miniature robot, in a realistic maze. Experimental results showed that, after familiarization of the environment, both grid cells and HD cells develop globally coherent firing maps by map calibration and activity correction. These results demonstrate that the hippocampus and the entorhinal cortex work together to form globally coherent metric representations of the environment. The underlying mechanisms of the hippocampal-entorhinal circuit in capturing the structure of the environment from sequences of experience are critical for understanding episodic memory.

Testing Self-organized Criticality across the Main Sequence Using Stellar Flares from TESS

Abstract Self-organized criticality describes a class of dynamical systems that maintain themselves in an attractor state with no intrinsic length or timescale. Fundamentally, this theoretical construct requires a mechanism for instability that may trigger additional instabilities locally via dissipative processes. This concept has been invoked to explain nonlinear dynamical phenomena such as featureless energy spectra that have been observed empirically for earthquakes, avalanches, and solar flares. If this interpretation proves correct, it implies that the solar coronal magnetic field maintains itself in a critical state via a delicate balance between the dynamo-driven injection of magnetic energy and the release of that energy via flaring events. All-sky high-cadence surveys like the Transiting Exoplanet Survey Satellite (TESS) provide the necessary data to compare the energy distribution of flaring events in stars of different spectral types to that observed in the Sun. We identified ∼106 flaring events on ∼105 stars observed by TESS at a 2 minute cadence. By fitting the flare frequency distribution for different mass bins, we find that all main-sequence stars exhibit distributions of flaring events similar to that observed in the Sun, independent of their mass or age. This may suggest that stars universally maintain a critical state in their coronal topologies via magnetic reconnection events. If this interpretation proves correct, we may be able to infer properties of magnetic fields, interior structure, and dynamo mechanisms for stars that are otherwise unresolved point sources.