dynamical systems theory - An area of mathematics used to describe the behavior of complex systems by employing differential and difference equations. Recently this approach has been advanced by some as the best way to describe human cognition.
No single theory about how self-organization operates is accepted across disciplines or within the field of human development. However, the concept has been used to consider the spontaneous emergence of order and new levels of complexity in physics, chemistry, mathematics, biology, and the study of human social groups. When systems are in a state of extreme disequilibrium, or disorganization, there is a tendency for the overall organization of the system to change. The concept of disequilibrium suggests that there are circumstances when the adaptive functions of the system are not adequate to address current fluctuations either internal to the system or external to the system.
~Newman & Newman Human Development text
Proponents of the dynamical systems theory approach to cognition believe that systems of differential or difference equations are the most appropriate tool for modeling human behavior. These equations are interpreted to represent an agent's cognitive trajectory through a high dimensional state space. In other words, cognition is explained as a multidimensional space of all possible thoughts and behaviors that is traversed by a path of thinking followed by an agent under certain environmental and internal pressures, all of which is captured by sets of differential equations. The terminology of dynamical systems theory is also adapted. Thus, cognition is spoken of in terms of state spaces; point, cyclic and chaotic attractors; trajectories; and deterministic chaos.
~Wiki & http://philosophy.uwaterloo.ca/MindDict/dynamicsystems.html
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