Bifurcations in Phase Space

Bifurcation means a division in two, a splitting apart, a change.  (Daveney, 1989, p. 80)

             A typical system bifurcation diagram is in Figure 1. Figure 18 shows the result of eight bifurcations of any dynamic system. To make it clearer to see, the Feigenbaum constant is not used and the bifurcations are instead shown equally spaced. One beginning trajectory ends with 256 possible outcomes. 

                Erickson’s eight developmental stages do not necessarily conflict with Jung. The eight developmental tasks of Erickson are essentially major bifurcations during our trajectory through life and result in 256 possible outcomes in the ego trajectory. Figure 19 shows these bifurcations along the ideal ego trajectory.  

            Jung also discussed critical stages in our life. These are shown as bifurcations in Figure 20. Figures 19 and 20 suggest that consciousness does not mature properly when developmental tasks are failed.

             Figure 21 looks closer at Erickson’s first developmental task, that of trust versus mistrust. A few of the possible changes to the ego trajectory are shown through the phase space. Many possibilities exist. The trajectory can bypass the unstable region or basin of this attractor, creating what chaos theory calls saddle points, or it can split off onto new trajectories. In the example shown in Figure 21, a very simplified trust versus mistrust bifurcation region is shown. Main possible alternative outcomes are:

            (1) regaining the original trajectory,

            (2) creating the nucleus of the borderline personality disorder,

            (3) creating the nucleus of the antisocial personality disorder, and

            (4) regression back to an earlier state. 

            The ego, unlike the physical body, can become stuck at any point (fixation) or can return back in time to a previous state (regression). Both fixation and regression are chaotic unstable states.