Dynamical Systems

Dynamical systems theory enters the depth-psychology corpus not as a peripheral borrowing from physics but as a constitutive framework for understanding how mind, brain, and self are organized in time. Thompson’s enactive biology provides the most technically rigorous treatment, distinguishing between dynamical systems as actual world-entities and as mathematical models, and deploying coordination-dynamics research — Haken, Kelso, and colleagues — to demonstrate how cognitive and motor behaviors emerge through bifurcations, phase transitions, and hysteresis rather than through static rule-following architectures. Siegel imports the nonlinear dynamical system vocabulary directly into developmental neuroscience, treating the brain as a self-organizing complex system whose emergent properties — states of mind, integration, interpersonal coordination — are lawfully intelligible only through dynamical analysis. Schore extends this into affective neuroscience, showing that chaotic sensitivity and small perturbations are precisely the mechanisms enabling flexible transitions between psychobiological states. At the more speculative margins, Ulanov draws on chaos theory’s period-doubling cascades, strange attractors, and fractal geometry to argue that Jungian symbols resemble the outputs of complex dynamical iteration. The productive tension across these positions concerns whether dynamical-systems language describes psychological phenomena genuinely or merely metaphorically — a question that remains unresolved but generative throughout the corpus.

In the library 19 passages

The brain is a complex system whose processes organize its functioning. That is, a complex system has an ‘emergent property’ that arises from the interaction of its basic constituents. This property is called ‘self-organization.’

Siegel formally introduces the dynamical system framework as the foundational model for understanding how brain and mind self-organize, linking it explicitly to states of mind and interpersonal functioning.

Siegel, Daniel J., The Developing Mind: How Relationships and the Brain Interact to Shape Who We Are, 2020thesis

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A dynamic system in the sense of a model, however, is a mathematical construction that aims to describe and predict the way an actual system changes over time.

Thompson draws the foundational distinction between dynamical systems as real-world phenomena and as mathematical models, establishing the conceptual basis for dynamicist cognitive science.

Thompson, Evan, Mind in Life: Biology, Phenomenology, and the Sciences of Mind, 2007thesis

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As the speed gradually increases, the in-phase pattern becomes unstable, and eventually at a certain critical frequency the fingers spontaneously switch to an anti-phase pattern (the system undergoes a bifurcation).

Thompson demonstrates how Haken and Kelso’s coordination-dynamics research instantiates core dynamical-systems concepts — bistability, bifurcation, hysteresis — in empirical studies of motor behavior.

Thompson, Evan, Mind in Life: Biology, Phenomenology, and the Sciences of Mind, 2007thesis

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What the study of coordination dynamics has provided, however, is considerable evidence that certain aspects of social interactions can be addressed in the language of self-organizing, dynamical processes.

Siegel extends coordination-dynamics analysis to interpersonal systems, arguing that dyadic social interaction is itself governed by self-organizing dynamical laws.

Siegel, Daniel J., The Developing Mind: How Relationships and the Brain Interact to Shape Who We Are, 2020thesis

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Chaotic systems are extremely sensitive to small perturbations, and that these tiny feedback perturbations control trajectories in chaotic systems… one can switch between a rich variety of dynamical behaviors as circumstances change.

Schore marshals dynamical-systems chaos theory to argue that psychobiological flexibility — the capacity to transition fluidly between affective states — depends on the system’s sensitive nonlinear responsiveness.

Schore, Allan N., Affect Regulation and the Origin of the Self: The Neurobiology of Emotional Development, 1994thesis

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Seeking to describe complex dynamic systems previously beyond the scope of classical mathematics and physics, the hard sciences are beginning to speak a language remarkably similar to Jung’s.

Ulanov argues that chaos theory’s treatment of complex dynamic systems converges with Jungian symbolic language, suggesting deep structural resonances between depth psychology and nonlinear science.

Ulanov, Ann Belford, The Feminine in Jungian Psychology and in Christian Theology, 1971supporting

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Fractal attractors are dynamic in the fullest sense of the word. As chaotic dynamics stretch and fold in on themselves, leading to closed curves that both loop around in unpredictable ways and connect every point on the attractor with every other.

Ulanov uses strange-attractor geometry to characterize the self-similar, boundary-defying quality of chaotic dynamics, implicitly mapping this onto the structure of archetypal symbols.

Ulanov, Ann Belford, The Feminine in Jungian Psychology and in Christian Theology, 1971supporting

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The transition to chaos occurs so reliably that its appearance can actually be predicted, that is, when r = 3.5699456… each side of the parabola bifurcates.

Ulanov demonstrates the period-doubling route to chaos through iteration, using mathematical precision to argue that the emergence of complexity from simplicity is lawfully predictable — a principle she links to psychic transformation.

Ulanov, Ann Belford, The Feminine in Jungian Psychology and in Christian Theology, 1971supporting

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Chaotic systems are perhaps best — certainly most enjoyably — analyzed through the use of models. Because chaotic systems stretch and fold, they are basically feedback loops that build upon themselves.

Ulanov introduces iterative feedback as the defining structural feature of chaotic dynamical systems, distinguishing nonlinear from linear equations and opening the comparison with psychological complexity.

Ulanov, Ann Belford, The Feminine in Jungian Psychology and in Christian Theology, 1971supporting

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The dynamical mode… describes the system in terms of continuous, rate-dependent processes, and thus explicitly includes the flow of time.

Thompson contrasts the dynamical mode of description — continuous, time-embedded, process-oriented — with the linguistic-symbolic mode, situating dynamical systems theory within a broader philosophy of biology.

Thompson, Evan, Mind in Life: Biology, Phenomenology, and the Sciences of Mind, 2007supporting

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Bourgine and Stewart (2004) expand the tesselation-automaton model from two to three dimensions and give a mathematical treatment of the model as a random dynamical system.

Thompson documents how minimal autopoiesis can be formally modeled as a random dynamical system, pushing the boundary between biological self-organization and mechanistic description.

Thompson, Evan, Mind in Life: Biology, Phenomenology, and the Sciences of Mind, 2007supporting

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Dynamical inspection (in the form of a phase space known as a first-return map) showed that the distribution of the intervals followed a particular kind of unstable dynamic pattern.

Thompson reports empirical phase-space analysis of epileptic neural activity, demonstrating how dynamical inspection reveals unstable periodic orbits that covary with conscious mental states.

Thompson, Evan, Mind in Life: Biology, Phenomenology, and the Sciences of Mind, 2007supporting

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Chronometric techniques and dynamical systems analysis suggest that the SN, and the AI in particular, plays a critical and causal role in switching between the fronto-parietal CEN and the DMN.

Menon applies dynamical systems analysis to insula-network switching, providing empirical support for the view that large-scale brain-network transitions are dynamically organized.

Menon, Vinod, Saliency, switching, attention and control: a network model of insula function, 2010supporting

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Systems thinking is wholistic, organismic, or ecological. Rather than asking ‘What is this made of?’, systems thinkers ask, ‘How do the components of this function as a pattern?’

Schwartz traces the intellectual genealogy of systems thinking from organismic biology, establishing the holistic, relational epistemology that underlies dynamical approaches to mind and self.

Schwartz, Richard C, Internal Family Systems Therapy, 1995supporting

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Control systems, such as the systems involved in autonomic regulation, require feedback and feed-forward loops which are not part of the explanatory framework of conditioning theory.

Payne argues that somatic-experiencing therapy requires a process model grounded in feedback-loop dynamics rather than stimulus-response conditioning, implicitly invoking dynamical systems principles.

Payne, Peter, Somatic experiencing: using interoception and proprioception as core elements of trauma therapy, 2015supporting

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Bourgine and Stewart’s (2004) model of minimal autopoiesis as a random dynamical system… can be taken as a challenge to Rosen: what crucial feature of the living organization does this model leave out?

Thompson poses the random-dynamical-system model of autopoiesis as a challenge to Rosen’s organismic theory, flagging an open theoretical tension about what dynamical formalism can and cannot capture.

Thompson, Evan, Mind in Life: Biology, Phenomenology, and the Sciences of Mind, 2007aside

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Studies of the ‘default mode’… reveal the importance of integration in healthy brain function… if this DMN is not well integrated with the rest of the brain, it may lead to certain difficulties.

Siegel’s discussion of default mode network integration implicitly depends on dynamical systems concepts of linkage and differentiation, though the term is not foregrounded here.

Siegel, Daniel J., The Developing Mind: How Relationships and the Brain Interact to Shape Who We Are, 2020aside

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