Dynamic systems theory (DST) is a framework for understanding how complex systems change over time, not through a single cause or central controller, but through the interaction of many components influencing each other simultaneously. Originally rooted in mathematics and physics, it has become a powerful lens for studying everything from how infants learn to walk to how patients change during psychotherapy. The core idea is simple: new patterns of behavior or organization emerge from the interactions within a system, without anyone or anything directing the process from the top down.
The Core Idea: Self-Organization
The central principle of DST is self-organization. In a self-organizing system, the parts interact with each other and spontaneously create patterns at a larger scale. No blueprint is needed. No leader calls the shots. A flock of birds forms a coordinated shape in the sky not because one bird is in charge, but because each bird follows simple rules about spacing and direction relative to its neighbors. The same logic applies to non-living systems: crystals form, vortexes spin, and lasers produce coherent light, all through interactions among their components.
The term “self-organizing system” was coined by W. Ross Ashby in the early days of cybernetics to describe machines that could change their own organization. Since then, the concept has expanded far beyond machines. Physicist Hermann Haken used lasers as an example of self-organized light and built a field called synergetics around the study of self-organization in systems that are open and far from equilibrium. This work connected self-organization to phase transitions, those moments when a system shifts from one organized state to a qualitatively different one, like water turning to ice.
Key Concepts: Attractors, Control Parameters, and Bifurcations
DST uses a few technical concepts that are worth understanding because they show up across nearly every application of the theory.
An attractor is a stable state that a system tends to settle into. Think of a ball rolling into a valley: it naturally comes to rest at the bottom. That resting point is the attractor. In human behavior, a habitual way of moving, thinking, or reacting can function as an attractor. The system keeps returning to that pattern unless something changes significantly enough to push it out.
A control parameter is some variable in the system that, when it changes gradually, can eventually trigger a dramatic shift in behavior. The control parameter doesn’t dictate what the new pattern will be. It just pushes the system to a tipping point. For example, increasing the speed of a horse on a treadmill eventually causes it to shift from a trot to a gallop. Speed is the control parameter, but the gallop pattern isn’t “contained” in the speed itself. It emerges from the whole system of muscles, joints, and neural signals reorganizing.
A bifurcation is that tipping point. It’s the moment when a system shifts from one stable state to another, or when one attractor splits into two. Bifurcations explain why change in complex systems is often sudden rather than gradual. You can slowly turn up the heat under a pot of water for minutes with little visible change, and then suddenly it boils. In DST terms, the system underwent a bifurcation. Critically, these dramatic qualitative shifts can arise from smooth, quantitative changes in just one aspect of the system.
How DST Changed Developmental Science
The most influential application of DST outside physics and mathematics came through the work of Esther Thelen, who applied the framework to infant motor development in the 1980s and 1990s. Her research challenged the dominant view that development unfolds according to a genetically pre-programmed timetable, with the brain acting as a central controller that unlocks new abilities on schedule.
Thelen’s most famous example involved the newborn stepping reflex. If you hold a newborn upright with feet touching a surface, the baby will make stepping motions. This reflex disappears around three months of age, and the traditional explanation was that maturing brain centers actively inhibit this primitive reflex, or that it was simply programmed to vanish. Thelen proposed something different. She noticed that babies’ legs were getting heavier during those months as they gained body fat, but their muscles weren’t yet strong enough to lift the heavier limbs against gravity. The reflex hadn’t been switched off by the brain. It was being masked by a change in the body.
She tested this in two elegant experiments. In one, she added small weights to the legs of newborns who still had the stepping reflex. Stepping decreased significantly. In the other, she placed older infants whose stepping had already disappeared into water up to their chests, reducing the effective weight of their legs. Robust stepping reappeared. These results showed that the “disappearance” of stepping wasn’t a neural event at all. It was the product of multiple factors (leg mass, muscle strength, posture, gravity) interacting in real time. No single component was “in charge.”
This work, along with collaborations with Linda Smith, led to a broader rethinking of cognitive and motor development. Thelen and Smith argued that developing children are complex systems with many interacting elements spanning genetic, neural, behavioral, and social levels. Interactions among these elements are nonlinear and time-dependent, and they have an intrinsic tendency to create pattern. There is no need to build pattern into the system ahead of time through genetic programming or innate knowledge. Developing systems are inherently creative, organizing themselves around attractor states.
Brain and Body in Continual Dialogue
One of the most important conclusions from DST-informed developmental research is that the brain is not the “controller” of behavior. Instead, brain and body are in continual dialogue from moment to moment. The body’s physical properties (its weight, its proportions, how it interacts with surfaces and gravity) shape what the brain can do, and the brain in turn capitalizes on the dynamics of the body. This perspective, sometimes called embodied cognitive dynamics, stands in contrast to traditional information-processing models that treat the brain like a computer running programs, with the body as merely the hardware that executes commands.
Traditional developmental models tend to explain new abilities as the result of new mental representations or cognitive structures forming inside the child’s mind. DST flips this: new behaviors emerge from the interaction of all available components, including the body, the environment, the task at hand, and the child’s history of prior movements and experiences. A baby learning to reach for a toy isn’t simply executing a motor program stored in the brain. The reach emerges from the baby’s current arm strength, posture, motivation, the weight and position of the toy, and dozens of other factors converging in that moment.
Applications in Psychotherapy
DST has also been applied to understanding how people change during psychotherapy. In a study examining cognitive therapy for depression, researchers proposed that therapeutic change follows dynamic systems principles. They found that two factors predicted the most improvement by the end of treatment: less “protection” of existing depressive patterns and more “destabilization” of those patterns during sessions.
In practical terms, destabilization meant the therapy involved more emotional intensity, more exploration of the historical roots of current problems, exposure to multiple sources of new information that contradicted the depressive worldview, and repeated practice of new skills. The therapist’s role was to provide enough support and stability that the patient could tolerate this destabilization without being overwhelmed. This maps neatly onto DST concepts: the depressive pattern is an attractor state, the therapeutic interventions act as control parameters that gradually destabilize the old pattern, and improvement represents a bifurcation into a new, healthier attractor.
Applications in Robotics and AI
In robotics, DST-informed thinking shows up in how engineers design robots that learn complex physical skills. Rather than programming every movement explicitly, researchers embed prior knowledge about physical principles, motor primitives, and control hierarchies into the learning process. These structured assumptions guide the robot’s learning, much like the body’s physical properties guide an infant’s emerging movements.
This approach has been applied to robot table tennis, tactile manipulation, four-legged locomotion, and dynamic motor skills on humanoid arms. By building in knowledge about things like contact dynamics and modular control structures, robots can acquire versatile skills with far less training data than they would otherwise need. The underlying philosophy is deeply DST-flavored: behavior isn’t centrally commanded but emerges from the interaction of the system’s components with its environment, shaped by the physical constraints and opportunities the body provides.
How DST Differs From Traditional Models
The sharpest contrast between DST and traditional approaches comes down to where you locate the source of new behavior. In classical cognitive or maturational models, new abilities come from inside the organism: a new brain structure comes online, a new mental representation forms, a genetic program unfolds on schedule. Change is driven by a specific internal cause.
DST rejects this single-cause logic. Change emerges from the whole system. No single component is privileged as “the” cause. A small, gradual change in one part of the system can trigger a dramatic reorganization of the whole, and the same component that matters in one context may be irrelevant in another. This makes DST inherently contextual. It treats variability not as noise or error, but as a window into the system’s dynamics and a necessary ingredient for change.
This shift has practical consequences. If you’re trying to help a child develop a motor skill, a DST perspective suggests you shouldn’t just wait for the brain to “mature.” You might change the physical environment, alter the task demands, or adjust the child’s posture, any of which could be the control parameter that tips the system into a new pattern. The same logic applies to therapy, education, or rehabilitation: change the right constraint, and the system reorganizes itself.