Unifying Large- and Small-Scale Theories of Coordination

Coordination is a ubiquitous feature of all living things. It occurs by virtue of informational coupling among component parts and processes and can be quite specific (as when cells in the brain resonate to signals in the environment) or nonspecific (as when simple diffusion creates a source–sink dynamic for gene networks). Existing theoretical models of coordination—from bacteria to brains to social groups—typically focus on systems with very large numbers of elements (N→∞) or systems with only a few elements coupled together (typically N = 2). Though sharing a common inspiration in Nature’s propensity to generate dynamic patterns, both approaches have proceeded largely independent of each other. Ideally, one would like a theory that applies to phenomena observed on all scales. Recent experimental research by Mengsen Zhang and colleagues on intermediate-sized ensembles (in between the few and the many) proves to be the key to uniting large- and small-scale theories of coordination. Disorder–order transitions, multistability, order–order phase transitions, and especially metastability are shown to figure prominently on multiple levels of description, suggestive of a basic Coordination Dynamics that operates on all scales. This unified coordination dynamics turns out to be a marriage of two well-known models of large- and small-scale coordination: the former based on statistical mechanics (Kuramoto) and the latter based on the concepts of Synergetics and nonlinear dynamics (extended Haken–Kelso–Bunz or HKB). We show that models of the many and the few, previously quite unconnected, are thereby unified in a single formulation. The research has led to novel topological methods to handle the higher-dimensional dynamics of coordination in complex systems and has implications not only for understanding coordination but also for the design of (biorhythm inspired) computers

Multistability and metastability: understanding dynamic coordination in the brain

Multistable coordination dynamics exists at many levels, from multifunctional neural circuits in vertebrates and invertebrates to large-scale neural circuitry in humans. Moreover, multistability spans (at least) the domains of action and perception, and has been found to place constraints upon, even dictating the nature of, intentional change and the skill-learning process. This paper reviews some of the key evidence for multistability in the aforementioned areas, and illustrates how it has been measured, modelled and theoretically understood. It then suggests how multistability—when combined with essential aspects of coordination dynamics such as instability, transitions and (especially) metastability—provides a platform for understanding coupling and the creative dynamics of complex goal-directed systems, including the brain and the brain–behaviour relation

Metastable Coordination Dynamics of Collaborative Creativity in Educational Settings

Educational systems consider fostering creativity and cooperation as two essential aims to nurture future sustainable citizens. The cooperative learning approach proposes different pedagogical strategies for developing creativity in students. In this paper, we conceptualize collaborative creativity under the framework of coordination dynamics and, specifically, we base it on the formation of spontaneous multiscale synergies emerging in complex living systems when interacting with cooperative/competitive environments. This conception of educational agents (students, teachers, institutions) changes the understanding of the teaching/learning process and the traditional roles assigned to each agent. Under such an understanding, the design and co-design of challenging and meaningful learning environments is a key aspect to promote the spontaneous emergence of multiscale functional synergies and teams (of students, students and teachers, teachers, institutions, etc.). According to coordination dynamics, cooperative and competitive processes (within and between systems and their environments) are seen not as opposites but as complementary pairs, needed to develop collaborative creativity and increase the functional diversity potential of teams. Adequate manipulation of environmental and personal constraints, nested in different level and time scales, and the knowledge of their critical (tipping) points are key aspects for an adequate design of learning environments to develop synergistic creativity.This work was supported by the National Institute of Physical Education of Catalonia (INEFC), Generalitat de Catalunya. M.A. is supported by the project “Towards an embodied and transdisciplinary education” granted by the Ministerio de Educación y Formación Profesional of the Spanish government (FPU19/05693). J.A.S.K. is supported by NIMH Grant MH MH080838, the Davimos Family Endowment for Excellence in Science, and the Florida Atlantic University Foundation

Neural Responses to Complex Auditory Rhythms: The Role of Attending

The aim of this study was to explore the role of attention in pulse and meter perception using complex rhythms. We used a selective attention paradigm in which participants attended to either a complex auditory rhythm or a visually presented word list. Performance on a reproduction task was used to gauge whether participants were attending to the appropriate stimulus. We hypothesized that attention to complex rhythms – which contain no energy at the pulse frequency – would lead to activations in motor areas involved in pulse perception. Moreover, because multiple repetitions of a complex rhythm are needed to perceive a pulse, activations in pulse-related areas would be seen only after sufficient time had elapsed for pulse perception to develop. Selective attention was also expected to modulate activity in sensory areas specific to the modality. We found that selective attention to rhythms led to increased BOLD responses in basal ganglia, and basal ganglia activity was observed only after the rhythms had cycled enough times for a stable pulse percept to develop. These observations suggest that attention is needed to recruit motor activations associated with the perception of pulse in complex rhythms. Moreover, attention to the auditory stimulus enhanced activity in an attentional sensory network including primary auditory cortex, insula, anterior cingulate, and prefrontal cortex, and suppressed activity in sensory areas associated with attending to the visual stimulus

Beyond in-phase and anti-phase coordination in a model of joint action

In 1985, Haken, Kelso and Bunz proposed a system of coupled nonlinear oscillators as a model of rhythmic movement patterns in human bimanual coordination. Since then, the Haken–Kelso–Bunz (HKB) model has become a modelling paradigm applied extensively in all areas of movement science, including interpersonal motor coordination. However, all previous studies have followed a line of analysis based on slowly varying amplitudes and rotating wave approximations. These approximations lead to a reduced system, consisting of a single differential equation representing the evolution of the relative phase of the two coupled oscillators: the HKB model of the relative phase. Here we take a different approach and systematically investigate the behaviour of the HKB model in the full four-dimensional state space and for general coupling strengths. We perform detailed numerical bifurcation analyses and reveal that the HKB model supports previously unreported dynamical regimes as well as bistability between a variety of coordination patterns. Furthermore, we identify the stability boundaries of distinct coordination regimes in the model and discuss the applicability of our findings to interpersonal coordination and other joint action tasks