Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 16, No. 4, pp. 429-456. © 2012 Society for Chaos Theory in Psychology & Life Sciences. Nonlinear Bifurcations of Psychological Stress Negotiation: New Properties of a Formal Dynamical Model Lawrence R. Levy 1 , University of Western Ontario, London, ON, Canada, Weiguang Yao, Eastern Health - Cancer Care Program, St. John’s, Newfoundland, Canada, George McGuire, University of the Fraser Valley, Abbotsford, BC, Canada, Dan N. Vollick, University of British Columbia, Okanogan, BC, Canada, Jennifer Jetté, Alberta Health Services, Calgary, AL, Canada, Matthew J. Shanahan, James M. Hay, and Richard W. J. Neufeld, University of Western Ontario, London, ON, Canada Abstract: 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. Key Words: stress, coping, dynamical systems, decisional control INTRODUCTION Negotiation of psychological stress is deemed to comprise progressive transactions among environmental demands and threats to well-being (stressors), coping activity aimed at their resolution, and subjective evaluation of coping effectiveness (see, e.g., Monroe, 2008). Stress and coping variously have been 1 Correspondence address: Richard W. J. Neufeld, Department of Psychology, University of Western Ontario, 361-Windermere Rd., Westminster Hall, 3 rd floor east, London, Ontario, Canada, N6A 3K7. E-mail: rneufeld@uwo.ca 429