pressure leads to a global qualitative change in physical state. Analogously, the loss of topological equivalence occurs at the fixed point that, for examples, splits into two or explodes into a cyclic orbit in phase space. The same critical point behaviors and quantities occur in a wide variety of specific processes and their equations, and they are independent of the way the trajectories first arrived in the fixed point neighborhood. Once the system enters the regime of critical behavior, the predictive significance of its dynamical history is lost. This may also be the case for emergent psychiatric disorder (Mandell et al, 1985; Mandell and Selz, 1992; Ehlers, 1995; Paulus et al, 1996; Huber et al, 1999).
There are diagnostic patterns of behavior when a nonlinear system is in a neighborhood of a potential bifurcation. They include sudden and/or large jumps resulting from a small change in experimental conditions, the appearance of big baseline fluctuations (anomalously large variance), the lengthening of the time
on
required to relax following evoked or spontaneous perturbation (“critical slowing”), the same global change in state occurring at different values of the parameter when increasing versus decreasing a parameter’s value (“hysteresis”), the existence of some range of values of the observable that cannot be attained by manipulation of the parameter (“inaccessibility”) and the availability of two or more distinct states in the same parameter neighborhood (“modality”) (Thom, 1972; Arnold, 1984; Gilmore, 1981). It is perhaps relevant to polydrug psychopharmacology and clinical management that the higher the co-dimension (the greater number of effective parameters being manipulated), the greater the accessibility and control of selected state stability becomes with respect to difficult to obtain behaviors. Examples of the potential advantages of simultaneous manipulation of multiple influences have been
developed for affect disorder and anorexia nervosa (Callahan and Sashin, 1987).
As evidence for the independence of critical behavior from specific history, the qualitatively universal bifurcations along the four canonical routes to chaos manifest dimensionless ratios of parameter and phase space geometries between bifurcations. These ratios are quantitatively universal. The formalisms that rescale the distances from fixed points in parameter and observable spaces result in the
same picture across scale, a dilatational symmetry (also called self similarity or
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