Another finding of chaos theory is bifurcation
theory. A bifurcation
is a place or point of branching or forking into qualitatively new types of
behavior. It is usually a sudden change, rather than a slow and gradual
evolution. Furthermore, it is a transition of a non-linear system into a realm
where new laws dictate what will occur to the system (Barrow, 1988).
Dixon (1993) calls bifurcations, sensitive
decision points, or SDPís. He points out that, far away from an SDP, a
system can be well behaved, but as an SDP is approached, the systemís
trajectory becomes random and unpredictable.
Complex systems (dynamic systems with numerous interrelated parts) tend
to encounter bifurcations, which when amplified, can lead either to order or to
chaos (Briggs & Peat, 1989). As a complex system functions, over time, tiny
changes or perturbations (such as a single photon of energy, or a slight
fluctuation in temperature) can be iterated
(repeated) to a size that will result in a bifurcation and the system will then
take a new direction.
Bifurcations can be considered as critical
points (SDPs) in the life of a complex system. They points can either
cascade toward chaos, through a process called period
doubling, or stabilize the system in a new behavior through a series of feedback loops (such as autocatalysis,
cross catalysis, and autoinhibition)
so that the system once again is in harmony with its environment. A typical
bifurcation map is shown in Figure 1.
Figure 1. Typical
Changes to the ego correspond to bifurcation points when we consider the
ego as a complex system. According to Jung (1976), "The changes that may
befall a man are not infinitely variable; they are variations of certain
occurrences which are limited in number" (p. 294). When a conflicting
experience occurs, a corresponding archetype
(the organs or components of Jungís collective unconscious) will arise from
the unconscious and "will attract to itself the contents of
consciousness" (Jung, 1976, p. 294).
If we consider the ego as a complex system, then when a person reaches a
critical decision point in their life where they must decide which of two
possible choices to make, either consciously or unconsciously, they will have
encountered a bifurcation point. The number of the primary bifurcations of the
psyche, caused by the archetypes as attractors, are limited in number
for each of us. Because of this uniqueness, they stand out as important events
that we usually donít forget.