Complex Systems Research


Complex Adaptive Systems
Complexity Theory/Thinking/Science
Dynamical Systems Theory
General Systems Theory
Generative Science
Self-Organization Theory
Systems Research
Systems Science
Systems Thinking/Theory


Agents forming a unified whole in their interactions, relationships, or dependencies

Principal Metaphors

  • Knowledge is … range of possible activity
  • Knowing is … doing, being
  • Learner is … a complex system
  • Learning is … adapting
  • Teaching is … influencing, occasioning




As might be inferred from the list of alternative titles at the top of this page, we have collected a range of interconnected field and theories under the umbrella of Complex Systems Research. A complex system comprises a group of agents that forms a unified whole in their interactions, relationships, or dependencies. The emergent behavior of that grander unity is transcendent; it exceeds the possibilities of any agents on their own, and it cannot be predicted on the basis of the rules governing those agents. In this regard, critical notions include:
  • Self-Organization (Self-Organized Criticality) (Per Bak, Chao Tang, Kurt Wiesenfeld, 1980s) – a feature of a complex system that appears as relatively stable macro-behavior, even while micro-activity (i.e., interactivities of its subsystems) can vary dramatically. Self-Organized Criticality occurs without centralized control.
In addition to Self-Organization, definitions and descriptions of complex systems revolve around such terms as emergent, adaptive, nonlinear, irreducible, noncompressible, non-decomposable, multi-level, context-sensitive, and adaptive. Common, but not universal features of complex systems include having a memory, structurally coupling with other systems, and being nested in grander systems. A sense of the variety of these systems might be gleaned from the graphic below (created by Hiroki Sayama, Collective Dynamics of Complex Systems (CoCo) Research Group).
Beyond those listed in the above graphic, associated constructs and discourses include:
  • Agent-Based Modeling (Individual-Based Modeling) – a computational approach for studying the behavior of a system by simulating the actions of the agents that it comprises
  • Catastrophe Theory (René Thom, 1960s) – a mathematical theory that attends to sudden, significant changes that are triggered by very small changes. (In matters of learning, it has been applied to the relationship between performance and, for example, matters of anxiety or arousal.) Popularizations of the notion include:
    • Tipping Point (Malcolm Gladwell, 2000s) – a threshold point in a complex system at which multiple, very-diverse possibilities present themselves – and at which point an explosive and irreversible systemic transformation may occur. Within discussions of learning, the notion of Tipping Point is often invoked as a challenge to educational structures based on assumptions of smooth, incremental, linear progress.
    • Critical Juncture Theory – Defining “critical junctures” as major turning points in the evolution of some form or phenomenon, Critical Junction Theory is used in various Social Sciences (see Sociology) to identify, describe, and explain sociocultural structures and dynamics.
  • Chaos Theory (Edward Lorenz, 1960s) – a transdisciplinary field of scientific inquiry that is concerned with identifying and understanding patterns within the apparent randomness that can emerge in dynamical systems as small changes in conditions trigger disproportionate effects. Among many educators, Chaos Theory has been embraced to make sense of such phenomena as learners’ wildly different interpretations of very similar experiences, the hard-to-pin-down nature of the “teachable moment,” and the impossibility of “perfect lessons.” Prominent associated constructs include:
    • Butterfly Effect (Edward Lorenz, 1960s) – a quality of some complex systems whereby its state is massively dependent on its “initial conditions.” That is, based on an analogy to the triggering of a storm in one part of the world by the flapping of a butterfly’s wings in another part, the Butterfly Effect asserts that minor changes to its starting conditions can lead to major and unpredictable differences in outcomes in complex systems.
  • Fractal (Benoît Mandelbrot, 1980s) – a descriptive term that can be applied to any shape that has the same “bumpiness of detail” across multiple levels of magnification. That is, a Fractal does not appear simpler or more complicated when magnified or reduced. The notion has found some traction in discussions of learning, as it offers an alternative metaphor to those associated with Reductionism – that is, to the assumption that phenomena must get simpler when parsed or magnified. Associated constructs include:
    • Scale Invariance (Scale Independence) – the formation/appearance/use of the same structure at different scales (i.e., levels of magnitication).
    • Self-Similarity – a type of Scale Invariance in which an object resembles itself at different levels of magnification. (A familiar example is the way a tree branch can resemble the entire tree.)
  • Network Theory (various, 1990s) – Narrowly defined, Network Theory is the mathematical study of relationships of the unities in a system, typically resulting in the generation of image that is useful for extrapolating general properties of the system (e.g., How well can it learn?). More broadly, Network Theory offers insights into different types and dynamics of networks, including the realization that all complex systems have a decentralized network structure. That point is argued to be vital in discussions of learning and well-being, based on the assertion that learning systems are necessarily complex systems. This point is perhaps more comprehensible by comparing network structures, four basic types of which have been identified – all of which are represented in formal education in one way or another, and only one of which is associated with the phenomenon of learning:
    • Centralized Network – a network structure with a principal hub through which all relationships (e.g., flow of information, channeling of resources) are mediated. This network structure has the advantage of efficient distribution and communication. However, its disadvantages include that it is only as robust and only as flexible as the central hub. (See simplified image, below.)
    • Distributed Network – a network structure with tight and extensive local connectivity, but no largescale systemic connectivity, affording a netlike structure that is robust by in which distribution and communication are very inefficient. Phenomena with this structure are highly resistant to change. (See simplified image, below.)
    • Decentralized Network – a network structure that might be construed as having many centers – that is, a network in which each many nodes are, in a sense, the centers of their own networks. This network structure combines efficient communication with a robust structure, enabling considerable flexibility and high adaptability. Phenomena with decentralized network structures include languages, social networks, the Internet, and the brain. Decentralized Networks are the “fingerprints” of complex learning systems. (See simplified image, below.) Associated constructs include:
      • Centrality – a numeration-based strategy to compare and rank the significance of nodes in a Decentralized Network – for example, to identify highly influential people in a social network, the key hubs in the Internet, or superspreaders of a disease
      • Dynamic Networks (Adaptive Networks) – the study of robust, self-organizing networks. The domain blends research into system dynamics from Complex Systems Research with emerging insights from Network Theory.
      • Multi-Agent System (Multi-Agent Simulation) – a computational system comprising multiple, relatively autonomous agents in a Decentralized Network. Typically, a Multi-Agent System is designed to solve a problem or perform a search that is beyond the capacity of any single-agent system.
      • Scale-Free Network – a network in which the connectivity of the nodes follows a Power Law Distribution (see below). That is, Scale-Free Network has many nodes with few links and few nodes with many links.
      • Small-World Network – a type of network in which any given node is likely to be linked to neighboring nodes but much less likely to be linked to distant nodes, all in a manner that makes it possible to get from one node to any other node in a small number of links
    • Fragmented Network – a network structure that lacks meta-connectivity – that is, technically, not really a network at all. With regard to complex co-activity, this type of structure can have at least one use/advantage: it can afford isolated explosions of diversity within smaller clusters that might, at some point, come together into a grander network. (See simplified image, below.)
  • Power Law Distribution – a mathematical model used to describe those phenomena that have large numbers of small items/members/events and small number sof large items/members events, thus indicating that small occurrences are common and larger occurrences are rare. Examples include wealth distribution, earthquakes, learning events, wars, Internet hubs, social trends, life-forms, and, articulations. Mathematically, one quantity varies as a power of another.
  • Systems Biology – an interdisciplinary domain that embraces a holistic approach in the study of the complex dynamics within biological systems. Associated constructs include:
    • Holobiont – a synergetic collective composed of interacting organisms from different species
    • Superorganism (Supraorganism) – a synergetic collective composed of interacting organisms of the same species
  • Systems Philosophy – an academic domain focused on bringing principles of Complex Systems Research to bear on philosophy
  • World-Systems Theory (World-Systems Analysis; World-Systems Perspective) (Immanuel Wallerstein, 2000s) – a systems-based approach to societal evolution and world history


There is a piece of common wisdom that floating around the sciences that John Barrow summarized as follows: “Arguments against new ideas generally pass through three distinct stages, from, ‘It’s not true,’ to, ‘Well, it may be true, but it’s not important,’ to, ‘It’s true and it’s important, but it’s not new – we knew it all along.’ That pretty much sums up commentaries on Complex Systems Research. All three categories of criticism can be found in contemporary discourses.

Authors and/or Prominent Influences

Yaneer Bar-Yam; Albert-Laszlo Barabasi; Gregory Bateson; Ludwig von Bertalanffy; Murray Gell-Mann; John Holland; Stuart Kauffman; Melanie Mitchell; Steven Strogatz; Duncan Watts; Stephen Wolfram

Status as a Theory of Learning

With regard to the concerns and foci of education, Complex Systems Research might be described as offering a meta-theory of learning – as the graphic below is intended to suggest.   learningecosystems

Status as a Theory of Teaching

Complex Systems Research is not a theory of teaching.

Status as a Scientific Theory

Complex Systems Research is a robust are of scientific inquiry.


  • Agent-Based Modeling (Individual-Based Modeling)
  • Butterfly Effect
  • Catastrophe Theory
  • Centrality
  • Centralized Network
  • Chaos Theory
  • Critical Juncture Theory
  • Decentralized Network
  • Distributed Network
  • Dynamic Networks (Adaptive Networks)
  • Fractal
  • Fragmented Network
  • Holobiont
  • Multi-Agent System (Multi-Agent Simulation)
  • Network Theory
  • Power Law Distribution
  • Scale Invariance (Scale Independence)
  • Scale-Free Network
  • Self-Organization (Self-Organized Criticality)
  • Self-Similarity
  • Small-World Network
  • Superorganism (Supraorganism)
  • Systems Biology
  • Systems Philosophy
  • Tipping Point
  • World-Systems Theory (World-Systems Analysis; World-Systems Perspective)

Map Location

Please cite this article as:
Davis, B., & Francis, K. (2022). “Complex Systems Research” in Discourses on Learning in Education.

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