In the mathematical formulation of complex systems within the framework of synergetics one distinguishes between micro variables and macro-variables or order parameters that evolve over longer time-scales and to which the micro-variables adjust rapidly. The number of possible configurations of micro variables is beyond astronomical and therefore the dimension of the micro dynamical state space can be assumed to be infinite. A relatively small number of order parameters competes for influence over the micro-variables. That means the macro state space is often of a relatively low dimension. At least it appears so for a certain length of time during which no bifurcations or transitions to new attractor states will occur.
The complication occurs when either through internal adaptation or external changes in the environment control parameters change in a way that led to bifurcations. While elementary bifurcations for classical, low dimensional dynamical systems are well characterized [see e.g. Thom] this is not the case for complex, adaptive systems. There is always a possibility that new order parameters emerge through new modes of self-organization of the micro variables. This can even happen in the presence of the previous order parameters for instance through the availability of new resources or through spatial separation. Because of the intrinsically high dimensionality of the microscopic state space it can become very difficult to predict exactly which modes of behavior start to grow to become a new order parameter. The new order parameters then can contribute to an increase in the dimensionality of the macroscopic state space and allows new directions for the system to grow.