Coordination dynamics

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Coordination dynamics is a qualitative and quantitative field of scientific inquiry which investigates the principles and mechanisms of coordination within and among living things, including (but not limited to) genes, cells, brains, organisms, as well as human beings and the 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 complex systems, and “dynamics” 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.

The name ‘coordination dynamics’ was coined by Scott Kelso and his collaborators in the mid 1980’s following the successful theoretical/mathematical treatment of his experiments on human movement coordination. Since then, 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 a multilevel, interdisciplinary approach that incorporates methods from various fields including physics, biology, psychology, cognitive science, neuroscience, nonlinear dynamics and chaos theory, kinesiology, philosophy, and others.

Particularly in the life sciences, the problem of coordination is 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 aims to describe, explain and predict the creation and persistence of patterns of coordination formed by natural systems. Specifically, coordination dynamicists seek to identify the universal dynamical laws and principles by which natural systems operate at microscopic, mesoscopic, and macroscopic levels of description (REF). Natural systems may include genetic regulatory networks (REF), neuronal population systems (REF), motor control of human limb movements, 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 phenomena, 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, and 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, and even 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 also displaying a tendency to remain autonomous.

Some of the basic concepts of self-organization in nonequilibrium systems such as order parameters or collective variables, control parameters, stability, fluctuations and timescales have been shown to play a key role in coordination dynamics. Nonlinear dynamics is a central tool used 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 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 or phase transition), 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 explored by coordination dynamics. The reason is that rhythmic behavior is often a stable and reproducible aspect of behavior on multiple levels. 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. There are good reasons to suppose that the stable, persistent and self-sustaining nature of biology’s functional units are well represented by 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 or function can be achieved by variety of processes. In the brain, for example, many disparate neural pathways can be invoked 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 everchanging external environment.

Synergies/coordinative structures

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. In evolutionary theory, synergies have also been proposed as the significant unit of selection.

Informational coupling

An important empirical discovery in coordination dynamics is that the coupling or interactions among components in natural systems is informational in nature, transcending particular mediums in which interactions occur. 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, matter and information with its environment (also called a nonequilibrium system), can organize itself, without any external influence or agent responsible for the observed order. 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 are 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

A novel but ubiquitous aspect of coordination discovered when symmetries are broken or lowered is metastability. Metastability has come to play 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 a 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 then coordinate their behavior to produce a certain cognitive function, but also express their own individual behavior, allowing the brain to rapidly shift its functionality in order to make sense of the external world. In terms of 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 as ‘ghosts’ where the fixed points used to be.

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 phenomenon called symmetry breaking occurs. It is the combination of symmetry breaking and coupling among the components that gives rise to metastable coordination dynamics and the rich behavior that ensues.

the Haken-Kelso-Bunz model

(See Metastability in the brain article)

The HKB model was originally formulated to account for and explain bimanual finger movement coordination which were found to exhibit primitive features of self-organization, including multistability, instability, phase transitions and hysteresis (basic memory element). The HKB model is a foundational law of coordination dynamics in that it offered not only a mathematical description of observed coordination phenomena but also predicted new features of biological self-organization such as fluctuation enhancement and critical slowing down (in both behavioral measures and large-scale recordings of the human brain). HKB 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 the original context. From the model can be derived other forms of coordination, e.g. between humans and other species, humans and machines, etc.

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, one aspect may enhance the properties of another. In this sense, apparent contradictions or seeming 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 (Philosophy of Complex Systems Book for REFs):

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) state 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). Importantly, complementarity as an epistemological aspect of reality falls out of a scientific theory, viz. the metastable nature of coordination dynamics.

Applications of coordination dynamics

Neurosciences

The principles and mechanisms 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. Following Kelso’s proposals in Dynamic Patterns (1995), Bressler and Kelso (2001; 2016) hypothesize that cognition emerges from the metastable coordination dynamics of various large-scale networks of brain regions. Recently, Tognoli and Kelso (2014) 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) and Kelso, et al (1992) used magnetoencephalography (MEG) to record brain signals while investigating sensorimotor coordination. These studies revealed complex spatial patterns changing in time while changing a control parameter to induce phase transitions. Many other studies of brain coordination dynamics, both empirical and theoretical, have followed this seminal work. The discovery of phase transitions in the brain is important because: a) they are the simplest expression of spontaneous self-organization in complex, natural systems; b) they express the collective, coordinated behavior of very large numbers of elements (e.g. neurons); c) diverse arrangements of microscopic variables can produce the same outcome (‘degeneracy’ or functional equivalence principle); d) switching, basic decision-making, may be seen to occur without locating ‘switches’ somewhere in the nervous system; and e) they offer both a method (to identify key variables) and a mechanism for coordination within the brain and between brains.

Kinesiology and human movement

Originally, coordination dynamics was used to describe, explain, and predict how inter-limb 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 captured as order parameter dynamics.

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 called 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 science

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 phenomenon 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), to investigate social coordination among groups of eight people. Both experimentally and theoretically (with the development of a model), it was found that the metastable ordered coordination known in dyadic systems is preserved (and extended) in higher dimensional systems; that is, varying frequencies and coupling strengths produced 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) following early work by Zanone and Kelso (1992) 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 and the intrinsic dynamics of the individual learner play a central role in the relationship between the learner and environment and in determining change.

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.

Recently, a coordination dynamics model of fitness is being developed by Michael Mannino (REF). Central to this model is the notion that exploiting a variety of different coordinative movements of the body and its interaction with the environment can have an effect on coordinated patterns in the brain, thus affecting cognitive processes.

See also

• Metastability in the brain
• Phi complex
• Neural oscillation
• Motor coordination
• J.A. Scott Kelso
• Complex systems
• Nonlinear dynamics
• Network science
• Self-organization
• 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. A. S. (1995). Dynamic patterns: The self-organization of brain and behavior. MIT press. Jirsa, V. K., & Kelso, J.A. 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.

Fuchs, A., Jirsa, V.K., & Kelso, J.A.S. (2000). Theory of the relation between human brain activity (MEG) and hand movements. NeuroImage, 11, 359-369.

Jirsa, V. K., Fuchs, A., & Kelso, J.A.S. (1998) Connecting cortical and behavioral dynamics: Bimanual coordination. Neural Computation, 10, 2019-2045.

Jirsa, V.K, & Kelso, J.A.S. (2000) Spatiotemporal pattern formation in neural systems with heterogeneous connection topologies. Phys.Rev. E, 62, 8462-8465.

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

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

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

Kelso, J.A.S., DelColle, J. & Schöner, G. (1990). Action‑Perception as a pattern formation process. In M. Jeannerod (Ed.), Attention and Performance XIII, Hillsdale, NJ: Erlbaum, pp. 139‑169.

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.

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

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

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

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

Kostrubiec, V., Fuchs, A., & Kelso, J. A. S. (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.

Zanone, P.G. & Kelso, J.A.S. (1992). The evolution of behavioral attractors with learning: Nonequilibrium phase transitions. Journal of Experimental Psychology: Human Perception and Performance, 18/2, 403‑421.

Kelso, J. A. 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. A. S. (2008). Neuroimaging coordination dynamics in the sport sciences. Methods, 45(4), 325-335.

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