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Coordination Dynamics

Coordination dynamics is a qualitative and quantitative field of scientific inquiry which investigates the underlying universal principles of coordination within and among living things, including (but not limited to) genes, cells, brains, organisms and their movement, as well as human beings and systems which they create, such as social systems and economies. The word ‘coordination’ refers to the spatiotemporal ordering and organization of functionally coupled, interacting components in a system, and “dynamics” specifically refers to the mathematical machinery of nonlinear dynamics used in the field, but generally can also refer to the properties of change in the system such as, oscillation, phase transitions, pattern formation, self-organization, multistability and metastability.

Since the birth of the field in the mid 1980’s, coordination dynamics has flourished and developed into a field with far ranging applications, as the problem of coordination spans many areas of inquiry. Coordination dynamics is multilevel, as well as interdisciplinary approach in that in incorporates methods from various fields including physics, biology, psychology, cognitive science, neuroscience, nonlinear dynamics and chaos theory, kinesiology, philosophy, and others.

Contents

1.	Overview 2.	The Logic of Coordination Dynamics 3.	Core Principles/Ideas of Coordination Dynamics 1.	Collective variables 2.	Control Parameters 3.	Oscillation 4.	Degeneracy 5.	Informational coupling 6.	Synergies 7.	Self-Organization and Pattern Formation 8.	Metastability and Broken Symmetry 9.	Complementary nature 10.	The Haken-Kelso-Bunz (HKB) Model 4.	Philosophy of Coordination Dynamics 5.	Applications of Coordination Dynamics 1.	Neurosciences 2.	Kinesiology and Human Movement 3.	Economics and Social Coordination Sciences 4.	Sport Sciences 6.	See also 7.	External Links 8.	References

Overview

Particularly in the life sciences, the problem of coordination is almost ubiquitous, existing at nearly all levels of analysis. Understanding the underlying principles of how parts of a system coordinate their behavior is very important given the rise in popularity in complexity science over the last few decades.

Using theoretical analysis, mathematical modeling, and empirical experimentation, coordination dynamics proposes to describe, explain and predict the creation and persistence of patterns of coordination formed by, and between, natural systems. Specifically, coordination dynamicists seek to identify the universal dynamical laws and principles by which natural systems operate, at various levels of description, such as microscopic, mesoscopic, and macroscopic.(REF). Natural systems may include genetic regulatory networks(REF), neuronal population systems(REF), motor movements of human limbs, swarm behavior of birds(REF), people interacting in economies, and social situations like team sports and crowd behavior(REF).

A central property of these systems is that the individual components are coupled and exchange meaningful information which is context-specific to the system as a whole. It is this information exchange at local levels which allow for global phenomenon, like self organization and emergence, to be studied. One of the central goals of coordination dynamics is to understand and characterize the nature of this informational coupling: 1) within a certain part of a system, 2) between regional parts of system, or 3) between various kinds of systems and their environments. In many cases, the coupling of elements within a system changes over space and time, i.e., elements can become coupled, change the strength, direction, or nature of their coupling, or possibly become uncoupled.  In some cases, (see Metastability below), components can exhibit simultaneous tendencies to be coupled and uncoupled, that is, they can simultaneously remain integrated while having a tendency to remain autonomous.

Nonlinear dynamics is a central tool used in the field of coordination dynamics, and offers both qualitative and quantitative mathematical description of various kinds of coordinative behavior. Models of nonlinearly coupled nonlinear oscillators, for example, can take measurements from observations of systems, offer a theoretical explanation or account of those observations, and make predictions about new phenomena. Overall, coordination dynamics thus seeks to uncover the behavior of dynamic patterns formed by living systems in space and time.

The Logic of Coordination Dynamics ¬¬¬¬¬¬¬¬¬¬¬¬¬ Since the problem of coordination is ubiquitous throughout a variety of natural (biological) systems, the approach to understanding it makes use of a variety of methods. As a scientific endeavor, coordination dynamics proceeds by combining various modes of inquiry, including empirical observation and experimentation, theoretical analysis, and computational modeling. For example, in human brain and behavior studies, data from experimentation which yield information about the intrinsic neural dynamics of human brains, can be compared with computational models that generate data, which then can provide information about possible underlying mechanisms(REF).

In terms of mathematical modelling, coordination dynamics first seeks to identify the order parameters of a system that will be investigated. The choice of the variable is important and non-trivial as these variables characterize the formation and change of patterns in the system. Then, control parameters are identified, experimentally or theoretically, and when suitably varied (in the model or experiment), the system qualitatively changes its behavior, changing its own state. Importantly, the level of description is also important – e.g., properties that are considered macro-properties at one level may be described as micro-properties or meso-properties at another level. Whether or not these properties supervene on different levels is not completely understood (see Philosophy section below). Then, a dynamical system, or well-formed rule for how this variable changes over time is written as a model, incorporating control parameters which govern how various properties of the system change.

Core Ideas of Coordination Dynamics

Collective variables

Collective variables (also termed order parameters) are state variables which capture quantifiable, measurable relations between the individual elements in a system. These local elements interact and cooperate in such ways as to produce global relational properties which do not exist in the elements themselves. For example, this may be the relative phase existing between interacting oscillation patterns of neuronal populations(REF). Global phenomena may reciprocally exert a causal influence on the individual elements, in turn changing their behavior. Mathematically, collective variables are usually represented as derivatives or instantaneous rates of change governed by functions in a n-dimensional system.

Control parameters

Control parameters are endogenous features of a system, or exogenous environmental conditions, which, when varied, qualitatively change the behavior and patterns the system under investigation produces. In some cases, small changes in control parameters may produce much larger variations in what a system is doing, and qualitatively change the behavior (called a bifurcation), whereas other times, changes in the values of the control parameters may not have much of an effect.

Oscillation

In many systems, oscillation, the repetitive back and forth change in time between states of a system, is a central feature of all systems explored by coordination dynamics. Oscillatory patterns are general features of change by which many systems can be characterized, including, neurons, human limbs, organisms (e.g., in predator-prey models), and movement within systems in general. In his book, Dynamic Patterns, Scott Kelso describes the functional role of oscillation as a “collective phenomenon” – as something that needs to be understood or studied in the system as a whole. The nature of oscillation is well captured by nonlinear dynamics, for example, with limit cycles in phase space.

Degeneracy

Degeneracy is an important concept in coordination dynamics and refers to the ability of a (biological) system to manifest a function or outcome in a variety of different ways. In other words, the same goal can be achieved by variety of processes. In the brain, for example, many disparate neural pathways can be invoked in to achieve a specific motor act (REF). Degeneracy allows for great flexibility and variability in achieving desired outcomes, which is useful for how organisms proceed and evolve in an ever changing external environment.

Synergies

A synergy is an emergent and collective functional structure or grouping of elements in a system which interact as single unit (REF). Synergies are the functional units in coordination dynamics and understood to be a central feature in increasingly complex systems. Using the same components within a system a variety of objectives may be accomplished, or likewise, the same goal can be accomplished with different components, and so synergies are a mechanism used to achieve degeneracy. Synergies are context-dependent in that the individual components in the system are at one time used for a certain purpose of function, and at another time are used for something different.

Informational Coupling

An important concept in coordination dynamics is that the coupling or interactions among components in natural systems is informational. Information is meaningful, exchanged and modified between components in a useful way. This is opposed to information simply being encoded and manipulated as symbolic representations.

Self-Organization and Pattern Formation

An open system, i.e., one which exchanges energy and matter with its environment (also called a non-thermal equilibrium system), can organize itself, without any external influence or agent. In this context, ‘organize’ means the ability to produce spatially or temporally ordered, structured patterns, which may have the appearance of design. This organization arises from the internal dynamics of the system as well as its interaction with its environment. Central to self-organizing systems is the phenomena of phase transitions, when the physical properties of the system change abruptly or discontinuously via a control parameter change.

Metastability and Broken Symmetry

Metastability plays a central role in coordination dynamics in general, and in cortical (cognitive) coordination dynamics in particular (See Metastability in the brain article). In general, this refers to the simultaneous tendency for individual components of system to couple together and for the individual components to remain autonomous. In the brain, for example, different regions of the cortex, comprised of neuronal populations, can simultaneous couple and the coordinate their behavior to produce a certain cognitive function, but also express their own individual oscillatory behavior, allowing the brain to rapidly shift its functionality in order to make sense of the external world. In terms on nonlinear dynamics, a metastable regime, in phase space for example, is one where stable equilibria have been annihilated and no longer exist, yet areas of attraction persist where those fixed points were.

Metastability in coordination dynamics originates from the extended HKB model, where a term was introduced representing the intrinsic dynamics of each oscillator. When this term is non-zero, that is, when each oscillator contains its own unique intrinsic dynamics, a phenomena called breaking the symmetry occurs.

The Haken-Kelso-Bunz Model (See Metastability in the brain article)

The HKB model was originally formulated to account for, and explain bimanual finger movements undergoing phase transitions. The model is foundational law of coordination dynamics in that it offers a description of a set of observed phenomena in the form a mathematical statement. It was later extended, to include a symmetry breaking term as well as stochasticity. It was found that this extended model offered description, explanation, and prediction well beyond its original context. From the model can be derived other forms of coordination.

Complementary nature

The field of coordination dynamics emphasizes that living natural systems and their environments are complementary, in the sense that each, when seen in combination, enhance the properties of the other. In this sense, apparent contradictions or seemingly competing tendencies, for example, local and global properties of neurons, are really complementary (REF). Kelso and colleagues have extended the principle of complementarity in quantum physics from Neils Bohr, to structurally higher levels of organization such as brains, humans and their individual and collective behaviors.

Philosophy of Coordination Dynamics

Several specific and general philosophical questions are raised by the field of coordination dynamics, and have generated some research, among them (REF’s):

1.	What does it mean to say problem of coordination is universal? Are there epistemological limits to what coordination dynamics, as a methodology, can tell us about the world? 2.	What is the ontological status of relations between entities? Of collective variables? 3.	Are emergent properties real? 4.	Is self-organization required for “mind”? What are the necessary and sufficient conditions for self-organization? 5.	Is pattern-formation truly mind-independent? 6.	What is the explanatory scope and power of dynamical models like the HKB? 7.	What is the epistemology of coordination dynamics specifically, and complexity in general? 8.	What is the nature of causality in complex systems? 9.	What is the relationship between different levels of description of a system? Can certain properties supervene on others? 10.	What can coordination dynamics tell us about the nature of the mind and brain? 11.	What are the epistemological limits of modeling collective variables as quantities which depend upon the current (or previous) sate of the quantity? 12.	What is the complementary nature of coordination dynamics? Is complementarity a feature of the world? In this context, “complementary” refers to, or emphasizes, the relational qualities between elements investigated by coordination dynamics, e.g., mind and brain, animal and environment, person and society, local and global, competition and coordination, integration and segregation, etc. (REF). Kelso et al., use the squiggle (~) as a symbolic representation of complementarity. (REF).

Applications of Coordination Dynamics

Neurosciences

The principles of coordination dynamics have been used extensively in the field of neuroscience (including systems neuroscience, social neuroscience, computational and cognitive neuroscience), as different areas of the brain (the cortex specifically) engage in oscillation, phase transitions, self-organization, pattern formation and metastability. Bressler and Kelso (2001; 2016) propose that cognition emerges from the coordination dynamics of various large-scale networks of brain regions. Kelso and Tognoli (2017), and others, offer metastable coordination dynamics as a mechanism by which the brain operates at certain levels, making sense of its environment. Recording brain signals from two people in a dual EEG experiment, Tognoli et al., (2007) discovered one of the first example in social neuroscience of coordinated behavior between humans, termed the phi complex (see wiki article). In this study, a pair of oscillatory EEG components were found to favor both independent behavior and interpersonal coordination between subjects performing finger movements. Fuchs et al., (1992) used magnetoencephalography (MEG) to record brain signals while investigating sensorimotor coordination. The study reveals complex spatial patterns changing in time while changing a control parameter to induce bifurcations.

Kinesiology and Human Movement

Originally, coordination dynamics was used to describe, explain, and predict how inter-limb motor movements are coordinated in humans, as well as gait shifts in locomotion of animals. (REF) Modeling bimanual tasks such as simple human finger movements (or limb movements in general) as oscillators in and out of phase, Kelso and colleagues were able to uncover universal properties of coordinated systems (REF), including how these mechanisms are used by the brain when it is involved in producing motor acts, as well as accounting for phase transitions in rhythmic bimanual movements.

Coordination dynamics was recently used to explore the intricate movements involved in ballet dancing and the simple kicking movements of infants. In the case of ballet dancing, it was found that the complicated inter-limb movements of a ballet dancer can be reliably represented with only a few basic in-phase or anti-phase coordination patterns (REF). Fuchs and colleagues have shown that, in this case, a high-dimensional complex biological system, can operate with low-dimensional fundamental coordinative patterns.

In the case of the newborn kicking movements, coordination dynamics was used to explore the nature of a well-known experiment on infant development from Rovee and Rovee in 1969 on mobile conjugate reinforcement. When a mobile was coupled to the infant’s toe by a ribbon, the movements of the mobile are then caused by the infant kicking, and is then seen by the infant, thus reinforcing the behavior through feedback and producing more kicking movements. This behavioral experiment was then theoretically modelled with coordination dynamics, as the movements of both the infant’s leg and the mobile can be modeled as oscillators with a coupling function as the conjugate reinforcement. An analysis of the model revealed the specific patterns of coordination between the infant and its coupling to the environment, for example the model accounts for the fact that when the infant’s leg is coupled to the mobile, it increases the rate of kicking from visual feedback. In addition, the model makes specific predictions about the nature of the bidirectional coupling between the infant’s leg and the mobile.

Economics and Social Coordination Sciences

Oullier and colleagues (REF) have used the methods and tools of coordination dynamics to provide novel approaches to modelling and interpreting experimental results from brain activity during economic decision making in the field of neuroeconomics (REF). They have also explored social coordination dynamics, investigating the mechanisms and self-organized processes that take place in human social interactions and human bonding (REF), for example, between individual and collective levels. For example, the researchers were able to quantify the degree individuals remain influenced by a social encounter with the behavior of the group, a phenomena referred to as “social memory.”

Recently, Zhang et al., (2018) extended the traditionally dyadic experiments involving the coordination of two people or one person and a virtual partner (REF), and investigated the social coordination of the multi-frequency finger movements of eight people. Both experimentally and theoretically, it was found that the metastable ordered coordination known in dyadic systems is preserved in higher dimensional systems; that is, varying frequencies and coupling strengths produced various predicted forms of social coordination and collective behavior.

Sports Sciences

Jantzen and colleagues (REF) have explored the application of coordination dynamics to the sports sciences. Coordination dynamics offers a theoretical and empirical framework for analyzing the properties of neural processes during sports performance, including skill learning, as well as how these patterns breakdown due to sports related brain injuries. In their study, the role of neuroimaging in sports is analyzed from the perspective of coordination dynamics.

Kostrubiec and colleagues (REF) have used coordination dynamics to develop a dynamical systems account of sensorimotor learning, which provides a framework for how novel motor skills are acquired and how old skills are modified in new situations, indicating for example, how stability plays a central role in the relationship between the learner and environment.

It is speculated that coordination dynamics can be used to model team movement patterns as dynamical self-organizing systems and address how the constantly changing but coordinated movements of people on teams evolve.

See Also

•	Metastability in the Brain •	Phi Complex •	Neural Oscillation •	Motor coordination •	Electroencephalogram •	J.A. Scott Kelso •	Complex Systems •	Nonlinear Dynamics •	Network Science •	Self-Organization •	Cognitive Modeling •	Emergence •	Dynamical System

External Links

Human Brain and Behavior Laboratory Center for Complex Systems and Brain Science

References

Oullier, O., De Guzman, G. C., Jantzen, K. J., Lagarde, J., & Scott Kelso, J. A. (2008). Social coordination dynamics: Measuring human bonding. Social neuroscience, 3(2), 178-192.

Oullier, O., & Kelso, J. A. (2009). Social coordination, from the perspective of coordination dynamics. In Encyclopedia of complexity and systems science (pp. 8198-8213). Springer New York.

Dumas, G., de Guzman, G. C., Tognoli, E., & Kelso, J. S. (2014). The human dynamic clamp as a paradigm for social interaction. Proceedings of the National Academy of Sciences, 111(35), E3726-E3734.

Kelso, J. S. (1997). Dynamic patterns: The self-organization of brain and behavior. MIT press. Jirsa, V. K., & Kelso, S. (Eds.). (2013). Coordination dynamics: Issues and trends. Springer.

Fuchs, A., & Jirsa, V. K. (Eds.). (2007). Coordination: neural, behavioral and social dynamics. Springer Science & Business Media.

Fuchs, A. (2014). Nonlinear dynamics in complex systems. Springer.

Zhang, M., Kelso, J. S., & Tognoli, E. (2018). Critical diversity: Divided or united states of social coordination. PloS one, 13(4), e0193843.

Kelso, J. S., & Fuchs, A. (2016). The coordination dynamics of mobile conjugate reinforcement. Biological cybernetics, 110(1), 41-53.

Haken, H., Kelso, J. S., & Bunz, H. (1985). A theoretical model of phase transitions in human hand movements. Biological cybernetics, 51(5), 347-356.

Miles, L. K., Lumsden, J., Richardson, M. J., & Macrae, C. N. (2011). Do birds of a feather move together? Group membership and behavioral synchrony. Experimental brain research, 211(3-4), 495-503.

Kelso, J. S., & Engstrom, D. A. (2006). The complementary nature. MIT press.

Fingelkurts, A. A., & Fingelkurts, A. A. (2004). Making complexity simpler: multivariability and metastability in the brain. International Journal of Neuroscience, 114(7), 843-862.

Fuchs, A., & Jirsa, V. K. (2000). The HKB model revisited: how varying the degree of symmetry controls dynamics. Human Movement Science, 19(4), 425-449.

Schoner, G., & Kelso, J. A. (1988). Dynamic pattern generation in behavioral and neural systems. Science, 239(4847), 1513-1520. Tognoli, E., Lagarde, J., DeGuzman, G. C., & Kelso, J. S. (2007). The phi complex as a neuromarker of human social coordination. Proceedings of the National Academy of Sciences, 104(19), 8190-8195.

Beek, P. J., Peper, C. E., & Daffertshofer, A. (2002). Modeling rhythmic interlimb coordination: Beyond the Haken–Kelso–Bunz model. Brain and cognition, 48(1), 149-165.

Fuchs, A., & Kelso, J. S. (2018). Coordination Dynamics and Synergetics: From Finger Movements to Brain Patterns and Ballet Dancing. In Complexity and Synergetics (pp. 301-316). Springer, Cham.

Kelso, J. S., Southard, D. L., & Goodman, D. (1979). On the coordination of two-handed movements. Journal of Experimental Psychology: Human Perception and Performance, 5(2), 229.

Kelso, J. S., & Tognoli, E. (2009). Toward a complementary neuroscience: metastable coordination dynamics of the brain. In Downward causation and the neurobiology of free will (pp. 103-124). Springer, Berlin, Heidelberg.

Bressler, S. L., & Kelso, J. A. (2016). Coordination dynamics in cognitive neuroscience. Frontiers in neuroscience, 10, 397.

Bressler, S. L., & Kelso, J. S. (2001). Cortical coordination dynamics and cognition. Trends in cognitive sciences, 5(1), 26-36.

Kelso, J. S. (2008). An essay on understanding the mind. Ecological Psychology, 20(2), 180-208.

Kostrubiec, V., Fuchs, A., & Kelso, J. A. (2012). Beyond the blank slate: routes to learning new coordination patterns depend on the intrinsic dynamics of the learner—experimental evidence and theoretical model. Frontiers in human neuroscience, 6, 222.

Kelso, J. S., de Guzman, G. C., Reveley, C., & Tognoli, E. (2009). Virtual partner interaction (VPI): exploring novel behaviors via coordination dynamics. PloS one, 4(6), e5749.

Jantzen, K. J., Oullier, O., & Kelso, J. S. (2008). Neuroimaging coordination dynamics in the sport sciences. Methods, 45(4), 325-335.

Thelen, E., Kelso, J. S., & Fogel, A. (1987). Self-organizing systems and infant motor development. Developmental Review, 7(1), 39-65.

Kelso, J. A. S. (2001). Self-organizing dynamical systems.

Haken, H. (1978). SYNERGETICS-An Introduction: Nonequilibrium Phase Transition and Self-Organization in Physics. Chemistry and Biology.

Fuchs, A., Kelso, J. S., & Haken, H. (1992). Phase transitions in the human brain: Spatial mode dynamics. International Journal of Bifurcation and Chaos, 2(04), 917-939.