Bifurcations

            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 SDP’s. He points out that, far away from an SDP, a system can be well behaved, but as an SDP is approached, the system’s 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 Bifurcation Map.  

            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 Jung’s 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 don’t forget.