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.

[1]  J. Yorke,et al.  Dimension of chaotic attractors , 1982 .

[2]  R. M. Noyes,et al.  Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction , 1974 .

[3]  L Glass,et al.  Counting and classifying attractors in high dimensional dynamical systems. , 1996, Journal of theoretical biology.

[4]  N. Bolger,et al.  Diary methods: capturing life as it is lived. , 2003, Annual review of psychology.

[5]  K. Heller,et al.  Measures of perceived social support from friends and from family: Three validation studies , 1983, American journal of community psychology.

[6]  J. Sprott.  Chaotic dynamics on large networks. , 2008, Chaos.

[7]  R W Neufeld,et al.  A dynamic vulnerability perspective on stress and schizophrenia. , 1992, The American journal of orthopsychiatry.

[8]  D. Broadbent,et al.  The Cognitive Failures Questionnaire (CFQ) and its correlates. , 1982, The British journal of clinical psychology.

[9]  J. Blascovich.  Challenge and Threat , 2008 .

[10]  J. Averill.  Personal control over aversive stimuli and its relationship to stress. , 1973 .

[11]  R. Neufeld,et al.  Application of process models in assessment psychology: Potential assets and challenges. , 1998 .

[12]  John M. Kelley,et al.  Measurement of stress appraisal. , 1995 .

[13]  D. S. Holmes,et al.  Behavior control over aversive events: does control that requires effort reduce anxiety and physiological arousal? , 1980, Journal of personality and social psychology.

[14]  M. Gunnar,et al.  The neurobiology of stress and development. , 2007, Annual review of psychology.

[15]  Y Shoda,et al.  Reconciling processing dynamics and personality dispositions. , 1998, Annual review of psychology.

[16]  R W Neufeld,et al.  A formal analysis of stressor and stress-proneness effects on simple information processing. , 1994, The British journal of mathematical and statistical psychology.

[17]  A. Heathcote.  Book review: Nonlinear dynamics: techniques and applications in psychology by R. A. Heath , 2002 .

[18]  R. Duncan Luce,et al.  Several unresolved conceptual problems of mathematical psychology , 1997 .

[19]  Robert C. Gardner,et al.  Data aggregation in evaluating psychological constructs: multivariate and logical deductive considerations , 1990 .

[20]  Steven J. Schiff,et al.  Differentiation of linearly correlated noise from chaos in a biologic system using surrogate data , 1992, Biological Cybernetics.

[21]  Randolph J. Paterson,et al.  What Are My Options?: Influences of Choice Availability on Stress and the Perception of Control , 1995 .

[22]  Richard W. J. Neufeld,et al.  Dynamic differentials of stress and coping , 1999 .

[23]  David Schuldberg,et al.  Social-support moderated stress: a nonlinear dynamical model and the stress-buffering hypothesis. , 2011, Nonlinear dynamics, psychology, and life sciences.

[24]  M Molnár,et al.  Dimensional complexity of the EEG in subcortical stroke--a case study. , 1997, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[25]  Stephen J. Guastello,et al.  Chaos and complexity in psychology: The theory of nonlinear dynamical systems. , 2008 .

[26]  Robert D. Winsor,et al.  Marketing under conditions of chaos: Percolation metaphors and models , 1995 .

[27]  Michael W. Eysenck,et al.  Anxiety and attention , 1988 .

[28]  R W Neufeld,et al.  Clear danger: situational determinants of the appraisal of threat. , 1987, Psychological bulletin.

[29]  Christopher Essex,et al.  Estimation of chaotic parameter regimes via generalized competitive mode approach , 2002 .

[30]  R. Neufeld.  Composition and uses of formal clinical cognitive science. , 2007, Nebraska Symposium on Motivation. Nebraska Symposium on Motivation.

[31]  Jeffrey M. Hausdorff,et al.  Multiscale entropy analysis of human gait dynamics. , 2003, Physica A.

[32]  S. Monroe,et al.  Modern approaches to conceptualizing and measuring human life stress. , 2008, Annual review of clinical psychology.

[33]  K. J. Anderson,et al.  Arousal and the inverted-U hypothesis: A critique of Neiss's "Reconceptualizing arousal." , 1990 .

[34]  Richard W. J. Neufeld,et al.  Facial electromyographic measures distinguish covert coping from stress response to stimulus threat , 1994 .

[35]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[36]  J. Coyne,et al.  Never the Twain shall meet? Closing the gap between coping research and clinical intervention research. , 2000, The American psychologist.

[37]  John E. R. Staddon,et al.  Social learning theory and the dynamics of interaction , 1984 .

[38]  Yuichi Nakamura,et al.  Approximation of dynamical systems by continuous time recurrent neural networks , 1993, Neural Networks.

[39]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[40]  Shirley Fisher,et al.  Stress And Strategy , 1986 .

[41]  Madalena Costa,et al.  Multiscale entropy analysis of complex physiologic time series. , 2002, Physical review letters.

[42]  P. Young,et al.  Emotion and personality , 1963 .

[43]  Neil B. Rappaport,et al.  A daily stress inventory: Development, reliability, and validity , 1987, Journal of Behavioral Medicine.

[44]  R. Neiss,et al.  Ending arousal's reign of error: A reply to Anderson. , 1990 .

[45]  Daniel D. Blaine,et al.  Modeling unipolar depression as a chaotic process. , 2003, Psychological assessment.

[46]  Sommers,et al.  Chaos in random neural networks. , 1988, Physical review letters.

[47]  Richard W J Neufeld,et al.  Coping with stress through decisional control: quantification of negotiating the environment. , 2010, The British journal of mathematical and statistical psychology.

[48]  David Schuldberg,et al.  Dynamics and Correlates of Microscopic Changes in Affect , 2002 .

[49]  A. J. Grimes.  Normal Accidents: Living with High Risk Technologies , 1985 .

[50]  R. M. Noyes,et al.  Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system , 1972 .

[51]  Ronald L. Greene,et al.  Nonlinear Physics with Maple for Scientists and Engineers , 1997 .

[52]  R W Neufeld,et al.  The economy of probabilistic stress: interplay of controlling activity and threat reduction. , 1988, The British journal of mathematical and statistical psychology.

[53]  Gillian H. Ice,et al.  Measuring stress in humans : a practical guide for the field , 2006 .

[54]  P. Klumb,et al.  Cognitive failures and performance differences: validation studies of a German version of the cognitive failures questionnaire. , 1995, Ergonomics.

[55]  H. Haken.  Synergetics: an Introduction, Nonequilibrium Phase Transitions and Self-organization in Physics, Chemistry, and Biology , 1977 .

[56]  Pei Yu.  Chapter 1 Bifurcation, Limit Cycle and Chaos of Nonlinear Dynamical Systems , 2006 .

[57]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[58]  I. Prigogine,et al.  From Being to Becoming: Time and Complexity in the Physical Sciences , 1982 .

[59]  Richard W. J. Neufeld,et al.  Stochastic dynamics of stimulus encoding in schizophrenia: Theory, testing, and application , 2010 .

[60]  Goran Opacic,et al.  A mathematical model of stress reaction: Individual differences in threshold and duration , 2000, Psychobiology.

[61]  J C Sprott,et al.  Dynamical models of happiness. , 2005, Nonlinear dynamics, psychology, and life sciences.

[62]  Grégoire Nicolis,et al.  Self-Organization in nonequilibrium systems , 1977 .

[63]  P. Holmes,et al.  MODELING A SIMPLE CHOICE TASK: STOCHASTIC DYNAMICS OF MUTUALLY INHIBITORY NEURAL GROUPS , 2001 .

[64]  Richard W. J. Neufeld,et al.  Coping with stress, coping without stress, and stress with coping: On inter-construct redundancies , 1990 .

[65]  Richard W. J. Neufeld,et al.  Decision-theoretic aspects of stress arousal and coping propensity , 1999 .

[66]  S. Thompson.  Will it hurt less if i can control it? A complex answer to a simple question. , 1981 .

[67]  Martin Casdagli,et al.  Nonlinear prediction of chaotic time series , 1989 .

[68]  Robert L. Borrelli.  Differential equations : a modelling perspective / Robert L. Borrelli, Courtney S. Coleman , 1986 .

[69]  S. Folkman,et al.  Stress, appraisal, and coping , 1974 .

[70]  J. Hammersley,et al.  Percolation Processes and Related Topics , 1963 .

[71]  Lawrence,et al.  QUANTITATIVE RESPONSE TIME TECHNOLOGY FOR MEASURING COGNITIVE , PROCESSING CAPACITY IN CLINICAL STUDIES , 2007 .

[72]  Christopher Essex,et al.  Competitive Modes and their Application , 2006, Int. J. Bifurc. Chaos.

[73]  James Theiler,et al.  Using surrogate data to detect nonlinearity in time series , 1991 .

[74]  J. Rall.  Why Things Bite Back: Technology and the Revenge of Unintended Consequences. , 1997 .

[75]  Danka Savic,et al.  A mathematical model of the hypothalamo-pituitary-adrenocortical system and its stability analysis , 2005 .

[76]  M. Strevens.  Scientific Explanation , 2005 .

[77]  G. Burrows,et al.  Measurement of stress and arousal: validation of the stress/arousal adjective checklist. , 1983, British journal of psychology.

[78]  R W Neufeld,et al.  Sex differences in stress response: a multivariate analysis. , 1974, Journal of abnormal psychology.

[79]  J. Kerr,et al.  High and low intensity exercise and psychological mood states , 1997 .

[80]  Weldon A. Lodwick,et al.  Parameter Estimation and Assessing the Fit of Dynamic Models , 1992 .

[81]  An elegant chaos. , 2014, Nature.

[82]  David M Kreindler,et al.  The effects of irregular sampling and missing data on largest Lyapunov exponents. , 2007, Nonlinear dynamics, psychology, and life sciences.

[83]  R. Lazarus.  Psychological stress and the coping process , 1970 .

[84]  J. Roughgarden.  Theory of Population Genetics and Evolutionary Ecology: An Introduction , 1995 .

[85]  Z. Q. John Lu,et al.  Nonlinear Time Series: Nonparametric and Parametric Methods , 2004, Technometrics.

[86]  R. May.  Uses and Abuses of Mathematics in Biology , 2004, Science.

[87]  J. Doyne Farmer,et al.  Exploiting Chaos to Predict the Future and Reduce Noise , 1989 .