Nonlinear bifurcations of psychological stress negotiation: new properties of a formal dynamical model.

Dynamical systems analysis is applied to a nonlinear model of stress and coping (Neufeld, 1999). The model is composed of 6 order parameters and 11 control parameters, and integrates core constructs of the topic domain, including variants of cognitive appraisal, differential stress susceptibility, stress activation, and coping propensity. In part owing to recent advances in Competitive Modes Theory (Yao, Yu & Essex, 2002), previously intractable but substantively significant dynamical properties of the 6-dimensional model are identified. They include stable and unstable fixed-point equilibria (higher-dimensional saddle-node bifurcation), oscillatory patterns attending fixed-point de-stabilization, and chaotic behaviors. Examination of the nature of system fixed-point de-stabilization, in relation to its control parameters, unveils mechanisms of re-stabilization, and dynamic stability control. All identified dynamics emerge naturally from a system whose construction guideposts are lodged in the addressed content domain. Dynamical complexities therefore may be intrinsic to the present content domain, possibly no less so than in other disciplines where the presence of such attributes has been established.

Coping with stress through decisional control: quantification of negotiating the environment.

Coping with stress through 'decisional control' - positioning oneself in a multifaceted stressing situation so as to minimize the likelihood of an untoward event - is modelled within a tree-structure scenario, whose architecture hierarchically nests elements of varying threat. Analytic and simulation platforms quantify the game-like interplay of cognitive demands and threat reduction. When elements of uncertainty enter the theoretical structure, specifically at more subordinate levels of the hierarchy, the mathematical expectation of threat is particularly exacerbated. As quantified in this model, the exercise of decisional control is demonstrably related to reduction in expected threat (the minimum correlation across comprehensive parameter settings being .55). Disclosure of otherwise intractable stress-coping subtleties, endowed by the quantitative translation of verbal premises, is underscored. Formalization of decisional stress control is seen to usher in linkages to augmenting formal developments from fields of cognitive science, preference and choice modelling, and nonlinear dynamical systems theory. Model-prescribed empirical consequences are stipulated.