Catastrophe Theory Bibliography

Gary Horlacher, Ph.D.
Andrus Geronotology Center
University of Southern California
ghorlach@usc.edu

This started out as a handout that was prepared for the National Council on Family Relations (NCFR) poster presentation (modeling dynamic processes in the family sciences) in Minneapolis, Minnesota, November 2006. It is not comprehensive. I am continuing to add additional sources as I continue to work my way through this literature one article or book at a time. A fairly comprehensive review of books, dissertations, book chapters, journal articles, and conference reports on catastrophe theory for the period 1978-1985 is found in Guastello, 1987a (305 listings). That review aims at identifying sources that appeared since Poston & Stewart's (1978) earlier bibliography. Other reviews include: Guastello, 1987a, 1995, 2000, 2002 (work organizations); Roser, 2004 (economics); Scott, 1985 (clinical psychology). Although not complete, this bibliography may provide a resource that can be useful to others interested in catastrophe theory. Corrections or additions to this list are welcome.

Catastrophe theory is a mathematical theory of stability which proposed that stable systems with discontinuities could only take on a small number of elementary forms (Thom, 1975). Systems with a single order (cf. outcome, state, dependent) variable and between one and four control (cf. predictor, process) variables could only take one of four increasingly complex forms: fold, cusp, swallowtail, and butterfly catastrophes.

The theory was popularized by Zeeman (1976a). The largest number of papers were published in 1978, but popularity has trickled down after 1982, probably due to limitations in methodology. Subsequently some statistical methods have been developed and as these become more well established, work on catastrophe theory is likely to increase again. Only a few articles used the fold, swallowtail, or butterfly models while over 80% used the cusp model. Some non-technical introductions, for those new to catastrophe theory include: Woodcock & Davis, 1978; Postle, 1980; Zeeman, 1976.

Catastophe theory has been applied to a large spectrum of phenomena (basic examples: Woodcock & Davis, 1978). Guastello (1987b) referenced 84 studies that used catastrophe theory to model phenomena in the physical sciences, biological sciences, business & economics, psychology, and sociology. Only 6 were limited to the physical sciences, while 93 percent dealt with life science applications. Psychological applications (cognitive, clinical, developmental, occupational, etc.) seem to be the most prolific. Most early studies were published in the journal, Behavior Science. This bibliography started with these referenced studies and I have been adding to the list. It looks like there are still a number of studies that have yet to be added.

Themes

Behavioral & Social Psychology.

Animal aggression (Zeeman, 1976a)
Emotion (disagreeable/frustration, agreeable/hope/relief) during problem solving (Allen & Carifio, 1995)
Eye, saliva, & fear conditioning (Frey & Sears, 1978)
Self-pity (Zeeman, 1976a)
Dating constraints (Tesser, 1980)
Engagement, Disengagement, & Coping (Carver & Scheier, 2005)
Social behavior (Flay, 1978)
Interpersonal attraction (Flay, 1978)
Student/Management evaluations (Flay, 1978)
Research participants biases (Flay, 1978)
Anticipation & Predator Behavior (Dubois & Sabatier, 1999)
Belief/Fear in Paranormal (Lange & Houran, 2000)
Cycles of serial murderers (Lange, 1999)
Decisions & choices (Bonanno & Zeeman, 1988)
Mother-child interacting vocalization (Freedle, 1977)

Biological & Ecological.

Spruce Budworm population (Casti, 1982)
Morphogenesis (Thom, 1975; Woodcock, 1978)
Enzyme kinetics (Tanyi, 1982)
Enzyme denaturation (Kozak & Benham, 1974, Benham & Kozak, 1976, 1977, 1978)
B-Cell Stimulation, Immune System (Merrill, 1977, 1978, 1980a, 1980b)

Business & Economics (review: Rosser, 2004).

Market planning (Chidley, Lewis, & Walker, 1978)
Stock market (Zeeman, 1974; 1976a; critiqued in Zahler & Sussman, 1977 & Weintraub, 1983)
Economic Equilibrium (Balasko, 1978)
Inflation & Unemployment - Phillips Curve or Stagflation model (Fischer & Jammernegg, 1986; Jammernegg & Fischer, 1986)
Monopoly equilibria (Bonanno, 1987)
Business cycles (Varian, 1979)
Optimal control theoretic growth (Rosser, 1983)
Bank Failures (Ho & Saunders, 1980)
Urban & regional economies (Amson, 1975; Mees, 1975; Wilson, 1976; Dendrinos, 1979; Puu, 1979, 1981a, 1981b; Beckmann & Puu, 1985; Andersson, 1986)
Ecologic-economic systems (Clark, 1976; Jones & Walters, 1976; Walters, 1986; Wagener, 2003)
International finance (George, 1981)
Customer satisfaction (Oliva & Burns, 1978; Oliva, Oliver, & Bearden, 1995; Oliva, Oliver, & MacMillan, 1992)
Competitive dynamics (Dou & Ghose, 2006; Greshov, Haveman, & Oliva, 1993; Oliva, Day, & MacMillan, 1988; Kauffman & Oliva, 1994)
Adopting products (Herbig, 1991; Lange, McDade, & Oliva, 2001, 2004; Oliva, 1991, 1994)
Exchange rate (Creedy, Lye, & Martin, 1996)
Socialism-capitalism change (Rosser, Rosser, Guastello, & Bond, 2001)
Fisheries regulation (Jones & Walters, 1976; Rosser, 2002)
Purchasing decisions (Chidley, 1978; Smith, W. C., 1980, 1984)
Management decisions (Halal & Lasken, 1980)

Clinical (review: see Scott, 1985)

Anorexia (Zeeman, 1976a; Callahan, 1982a)
Adolescent smoking prevention (Byrne, Mazanov, & Gregson, 2001)
Adolescent alcohol use (Clair, 1998)
Alcohol relapse (Hufford, Kitkiewitz, Shields, Kodya, Caruso, 2003)
Alcohol’s relation to suicide (Hufford, 2001)
Drug addiction (Guastello, 1984b)
Affect response (Sashin, 1985)
Janov’s primal theory of neurosis (Postle, 1980)
Levels of consciousness – transcendental meditation (Postle, 1980)
Blame for assault (Lanza, 1999)

Developmental & Evolution.

Cognitive Development (Saari, 1977; van der Maas & Molenaar, 1992 [cf. Preece, 1980])
Developmental transitions (Hartelman, van der Maas, & Molenaar, 1998)
Sexual Orientation (Evans & Zeiss, 1985)
Evolution Theory (Zeeman, 1992; Dodson, 1975, 1976; Dodson & Hallam, 1977)
Kohlber'gs Moral Development Theory (Freedle, 1977)

Education & Learning (see also Developmental section above).

Higher education: faculty vitality, teacher expectations-student performance, student attrition-persistence (Staman, 1982)
Child learning (Boyes, 1988)
Degradation of validity due to learning skills (Keil & Cortina, 2001)
Problem solving in science (Stamovlasis, 2006)
Academic performance (Guastello, 1987)

Organizational-Industrial Psychology (overviews: Guastello, 1995, 2002).

Employee turnover (Sheridan, 1985; Sheridan & Abelson, 1983; Youngblood, Mobley, & Meglino, 1983)
Collective bargaining: Union/Management (Oliva, Peters, & Methen, 1981)
Management decision making (Carhart, 1984, Wright, 1983)
Organizational change (Baack & Cullen, 1992; Bigelow, 1982)
Within organization negotiation (Johnson, 1982)
Motivation (Job-Organization) Performance (Guastello, 1981, 1984b, 1984c)
Overtime for postal workers (Haslett, Moss, Osborne, & Ramm, 2000)
Production efficiency vs. waste (Guastello, 1982a, 1985b)
Work performance stress models: fatigue (Guastello, 1995; Guastello & McGee, 1987); diathesis-stress (periodicity in work week/24-hour circadian rhythm) (Guastello, 1982a, 1985b); buckling stress (Guastello, 1985a), ability stress (performance in sports) (Fazey & Hardy, 1988; Hardy, 1990, 1993; Hardy & Parfitt, 1991; Hardey et al. 1995?)
Personnel selection (Guastello, 1982b)
Emerging leadership (Guastello, 1998; Zaror & Guastello, 2000; Guastello & Bond, 2007)
Accident Processes (Guastello, 1987c, 1988a, 1989, 1991, 1992b; Guastello, Gershon, & Murphy, 1999)

Perception-Judgment.
(See occupational psychology for business decisions)

Ambiguous pictures (Poston & Stewart, 1977, 1978; Stewart & Peregoy, 1983; Ta'eed, Ta'eed, & Wright, 1988)
Perception thresholds (Yelen, 1980; Freedle, 1977)
Driving when intoxicated (Zeeman, 1976b)
Traffic behavior (Furutani, 1976)
Stearing behavior (Furutani, 1977)
Law decisions (Keown, 1980)
Attitude Transition (Flay, 1978; Wagenmakers, van der Maas, & Molenaar, 2005; van der Maas, Kolstein, & van der Pligt, 2003)
Pigeons decision making (Zeiler & Solano, 1982)
Prior information bias (Hanges, Braverman, & Rentsch, 1991)

Political-Sociological

Art & political censorship (Isnard & Zeeman, 1976)
Governmental support (Isnard & Zeeman, 1976)
Latin American politics (Adelman & Hihn, 1982)
Riot outbursts (Smith, J. Q., 1980; Zeeman, et al, 1976)
Military action (Zeeman, 1976a; Isnard & Zeeman, 1976; Morrow, 1982)
Public opinion (Jiobus & Lundgren, 1978)
Violence outburst (Jiobus & Lundgren, 1978)
Conflict & Cooperation – India/Pakistan 1948-1973 (Rummel, 1987)
War-peace & international violence – WWI, WWII (Holt, Job, & Markus, 1978)
Attitude change in Russia – Perestroika 1985-1991 (Smirnov & Ershov, 1992)

Critiques.

Alexander, Herbert, DeShone, & Hanges, 1992 (Guastello, 1987b, 1988; response Guastello, 1992)
Ayers, 1981 (Yelen, 1980)
Sussman & Zahler, 1978 (Isnard & Zeeman, 1977; responses… Guastello, 1981; Oliva & Capdevielle, 1980)
Weintraub, 1983 (Zeeman, 1974)
Kolata, 1977.
Horgan, 1995, 1997 (Rosser, 2004)

Methods.

Dynamic polynomial regression (Guastello, 1982a, 1982b, 1987b, 1988a, 1992a, 1992b, 1995)

Static nonlinear regression (Guastello, 1998; Guastello & Bond, 2007)

Multivariate Estimation Procedure - GEMCAT (Oliva, Desarbo, Day, & Jedidi, 1987; Lange, Oliva, & McDade, 2000; Lange, 2000)
Stochastic Modeling - Static (Cobb, 1978, 1980, 1981a, 1981b, 1981c, 1988; Cobb & Zacks, 1985, 1988 (time series); Cobb, Koppstein, & Chen, 1983; Cobb & Watson, 1980; Creedy & Martin, 1998; Lye & Martin, 1993) [Empirical examples: Stewart & Peregoy, 1983; Ta'eed, Ta'eed, & Wright, 1988; Hanges, Braverman, & Rentsch, 1991; Allen & Carifio, 1995]
Enhancements to Cobb's method: Level crossing & kernel density (Hartelman, 1997)
Time series & level crossing (Wagenmaker, Molenaar, Grasman, Hartelman, & van der Maas, 2005)
Following is a copy of an unpublished paper I wrote evaluating and reviewing the three primary methods listed above (Cobb's, Guastello's, & GEMCAT): Horlacher & Silverstein, 2007.

Mathematics & Graphics.

Catastrophe geometry (Woodcock & Poston, 1974)
Introduction to catastrophes (Fararo, 1978; Gilmore, 1981; Lu, 1976; Poston & Stewart, 1978; Saunders, 1980)
Stability of dynamical systems (Zeeman, 1988)
Classification theorem (Thom, 1975)
Others: Callahan, 1980, 1982b; Gilmore, 1979; Arnold, …
History of early catastrophe theory (Aubin, 2001, 2002?)
Asymmetric mixtures & catastrophes (Brus, 1988)

Applications to the Physical Sciences.

Review Articles (Stewart, 1981, 1982, 1983a, 1983b, 1984)
Review Books (Gilmore, 1981; Poston, & Stewart, 1978; Thompson, 1982)

Methodologies

When Thom first introduced Catastrophe Theory, he envisioned it being a methodology as well as a theory. Yet the methodological development has been much slower than the theoretical development. Methods used in each studies included in this review are noted. These studies can be organized according to three major groupings:

Theory. Most of the studies (55%) use catastrophe theory as a heuristic for integrating a variety of perspectives within a more general framework. These studies include face validity and are valuable for their theoretical integration capacity. They tend not to include data. Most of the studies that have been published to date fit into this category.
Hypothesis Testing. Many studies (27%) test various hypotheses that can be generated based on the relationships predicted by catastrophe theory. The most common of these is the five qualitative flags for the cusp model outlined by Gilmore (1981): hysteresis, discontinuity, bi-modality, divergence, and inaccessibility. Several studies look for these flags in their data. Other approaches include plotting the a-b (normal-splitting) variables and showing divergence of the distribution of the dichotomized outcome variable; plotting a-b variables as a function of time until a catastrophe occurs; etc.
Model Fitting. A small but increasing proportion of the papers dealing with catastrophe theory use statistically modeling (18%). These methods are interested in trying to fit data to the mathematical formula and checking the goodness of fit to the model. Three different directions have been taken in model fitting techniques. First is a multivariate regression approach by Oliva and colleagues. This method uses more than one variable to approximate a latent construct for the control variables. The second method by Guastello uses polynomial regression. The third approach is referred to as dynamic modeling and was led by Cobb, and more recently innovations have been suggested by Hartelman and colleagues.

Bibliography

Adelman, I., & Hihn, J. M. 1982. Politics in Latin America : A catastrophe theory model. Journal of Conflict Resolution, 26, 592-620.

Alexander, R. A., Herbert, G. R., DeShone, R. P., Hanges, P. J. 1992. An examination of least-squares regression modeling of catastrophe theory. Psychological Bulletin, 111, 366-374.

Allen, B. D., & Carifio, J. 1995. Nonlinear Analysis: Catastrophe theory modeling and Cobb's cusp surface analysis program. Evaluation Review, 19, 64-83.

Amson, J. C. 1975. Catastrophe theory: A contribution to the study of urban systems? Environment and Planning, B2, 177-221.

Andersson, Å. E. 1986. The four logistical revolutions. Papers of the Regional Science Association, 59, 1-12.

Ayres, T. J. 1981. Catastrophe theory and brightness judgments. Perception & Psychophysics, 29, 407.

Aubin, D. 2002? Forms of explanation in the catastrophe theory of Rene Thom: Topology, morphogenesis, and structuralism. In M. N. Wise (Ed.), Growing explanations: Historical perspective on the sciences of complexity (pp.95-130).

Aubin, D. 2001. From catastrophe to chaos. The modeling practices of applied topologists. In U. Bottazzini & A. D. Dalmedico (Eds.), Changing images in mathematics: From the French Revolution tothe new millenium (pp. 255-279). London: Routledge.

Baack, D., & Cullen, J. B. 1992. A catastrophe theory model of technological and structural change. Journal of High Technology Management Research, 3, 125-145.

Baker, J. S. & Frey, P. W. 1980. A cusp catastrophe: hysteresis, bimodality, and inaccessibility in rabbit eyelid conditioning. Learning and Motivation, 10, 520-535.

Balasko, Y. 1978. The behavior of economic equilibria: A catastrophe theory approach. Behavioral Science, 23, 375-382.

Beckmann, M. J., & Puu, T. 1985. Spatial economics: Density, potential, and flow. Amsterdam: North-Holland.

Benham, C. J., & Kozak, J. J. 1976. Denaturation: An example of a catastrophe II. Two-state transitions. Journal of Theoretical Biology, 63, 125-149.

Benham, C. J., & Kozak, J. J. 1977. Denaturation: An example of a catastrophe III. Phase diagrams for multistate transformations. Journal of Theoretical Biology, 66, 679-693.

Benham, C. J., & Kozak, J. J. 1978. Catastrophes in statistical biophysics. Behavioral Science, 23, 355-359.

Bigelow, J. 1982. A catastrophe model of organizing change. Behavioral Science, 27, 26-42.

Bonanno, G. 1987. Monopoly equilibria and catastrophe theory. Australia Economic Papers, 26:49, 197-215.

Bonanno, G., & Zeeman, E. C. 1988. Divergence of choices despite similarity of characteristics: An application of catastrophe theory. European Journal of Operational Research, 36, 379-392.

Bosserman, R. W. 1982. The internal security subsystem. Behavioral Science, 27, 95-103.

Boyes, E. 1988. Catastrophic misconceptions in science education. Phys. Educ., 23, 105-109.

Brus, T. 1988. Asymmetric mixtures and catastrophes. European Journal of Operational Research, 36, 371-378.

Bruter, C. P. 1978. The theory of catastrophes: Some epistemological aspects. Synthese, 39, 293-315.

Byrne, D. G., Mazanov, J., & Gregson, R. A. M. 2001. A cusp catastrophe analysis of changes to adolescent smoking behaviour in response to smoking prevention programs. Nonlinear Dynamics, Psychology, and Life Sciences, 5, 115-137.

Callahan, J. 1980. Bifurcation geometry of E₆. Mathematical Modelling, 1, 283-309.

Callahan, J. 1982a. A geometric model of anorexia and its treatment. Behavioral Science, 27, 140-154.

Callahan, J. 1982b. Special bifurcations of the double cusp. Proceedings of the London Mathematical Society, 45, 227-257.

Carver, C. S., & Scheier, M. F. 2005. Engagement, disengagement, coping, and catastrophe. In A. J. Elliot & C. S. Dweck (Eds.), Handbook of competence and motivation (pp. 527-547). Guilford : New York .

Casti, J. 1982. Catastrophes, control, and the inevitability of spruce budworm outbreaks. Ecological Modelling, 14, 293-300.

Chidley, J. 1978. Catastrophe theory in consumer attitude studies. Journal of the market research society, 18, 69-92.

Chidley, J., Lewis, P., Walker, P. 1978. The cusp catastrophe as a market planning aid. Behavioral Science, 23, 351-354.

Clair, S. 1998. A cusp catastrophe model for adolescent alcohol use: An empirical test. Nonlinear Dynamics, Psychology, and Life Sciences, 2, 217-241.

Clark, C. W. 1976. Mathematical Bioeconomics. New York: Wiley-Interscience. Cobb, L. 1978. Stochastic catastrophe models and multimodal distributions. Behavioral Science, 23, 360-374.

Cobb, L. 1978. Stochastic catastrophe models and multimodal distributions. Behavioral Science, 23, 360-374.

Cobb, L. 1980. Estimation theory for the cusp catastrophe model. Proceedings of the section on survey research (American Statistical Association), 1980, 772-776.

Cobb, L. 1981a. Parameter estimation for the cusp catastrophe model. Behavioral Science, 26, 75-78.

Cobb, L. 1981b. Stochastic differential equations for the social sciences. In Cobb & Thrall (Eds.), Mathematical frontiers of the social and policy sciences, Westview Press. (extended version on internet)

Cobb, L. 1981c. The multimodal exponential families of statistical catastrophe theory. In C. Taillie, G. P. Patil, & B. Baldessari (Eds.), Statistical distributions in scientific work (Vol. 4, pp. 37-68). Boulder , CO : Westview Press & AAAS.

Cobb, L. 1988. Statistical catastrophe theory. In S. Kotz & N. L. Johnson (Eds.), Encyclopedia of statistical sciences, Vol. 8 (pp. 634-640). New York: John Wiley.

Cobb, L. 1985/1998. An introduction to cusp surface analysis. Louisville, Colorado: Aetheling Consultants. (http://www.aetheling.com/models/cusp/Intro.htm)

Cobb, L., Koppstein, P., & Chen, N. H. 1983. Estimation and moment recursion relations for multimodal distributions of the exponential family. Journal of the American Statistical Association, 78, 124-130.

Cobb, L. & Watson, B. 1980. Statistical catastrophe theory: An overview. Mathematical Modelling, 1, 311-315.

Cobb, L., & Zacks, S. 1985. Applications of catastrophe theory for statistical modeling in the biosciences. Journal of the American Statistical Association, 80, 793-802.

Cobb, L., & Zacks, S. 1988. Nonlinear time series analysis for dynamical systems of catastrophe type. In R. Mohler (Ed.), Nonlinear time series and signal processing (pp. 97-118). New York: Springer-Verlag [Lecture Notes in Control and Information Sciences, 106].

Creedy, J. & Martin, V. L. 1998. Nonlinear modelling using the generalized exponential family of distributions. Bulletin of Economic Research, 50, 229-255.

Creedy, J., Lye, J., & Martin, V. L. 1996. A non-linear model of the real US/UK exchange rate. Journal of Applied Econometrics, 11, 669-686.

Dendrinos, D. S. 1979. Slums in capitalist urban settings: Some insights from catastrophe theory. Geographia Polonica, 42, 63-75.

Dockens, W. S. 1979. Induction/catastrophe theory: A behavioral ecological approach to cognition in human individuals.

Dodson, M. M. 1975. Quantum evolution and the fold catastrophe. Evolutionary Theory, 1, 107-118.

Dodson, M. M. 1976. Darwin's law of natural selection and Thom's theory of catastrophes. Mathematical Biosciences, 28, 243-274.

Dodson, M. M., & Hallam, A. 1977. Allopatric speciation and the fold catastrophe. The American Naturalist, 111, 415-433.

Dou, W., & Ghose, S. 2006. A dynamic nonlinear model of online retail competition using cusp catastrophe theory. Journal of Business Research, 59, 838-848.

Dubois, D. M., Sabatier, P. 1999. For a naturalist approach to anticipation: from catastrophe theory to hyperincursive modeling. International Journal of Computing Anticipatory Systems, 4, 35-59.

Evan, D., & Zeiss, A. M. 1985. Catastrophe theory: A topological reconceptualization of sexual orientation. New Ideas in Psychology, 2, 235-251.

Fararo, T. J. 1978. An introduction to catastrophes. Behavioral Science, 23, 291-317.

Fazey, J. A., & Hardy, L. 1988. The inverted-U hypothesis: A catastrophe for sport psychology. British Association of Sports Sciences Monograph, 1. Leeds, UK: The National Coaching Foundation.

Fischer, E. O., & Jammernegg, W. 1986. Empirical investigation of a catastrophe theory extension of the Phillips Curve. The Review of Economics and Statistics, 68, 9-17.

Flay, B. R. 1978. Catastrophe theory in social psychology: Some applications to attitudes and social behavior. Behavioral Science, 23, 335-350.

Freedle, R. 1977. Psychology, Thomian Topologies, Deviant Logics, and Human Development. In N. Datan & H. Reese (Eds.), Life-span developmental psychology: Dialectical perspectives on experimental research (pp. 317-341). New York: Academic Press.

Frey, P. W., Sears, R. J. 1978. Model of conditioning incorporating the Rescorla-Wagner Associative Axiom, a dynamic attention process, and a catastrophe rule. Psychological Review, 85, 321-340.

Fung, K. K. 1980. Benefits and costs of confidential Information: An application of systems theory and catastrophe theory. Behavioral Science, 25, 192-204.

Furutani, N. 1976a. A new approach to traffic behavior: I. Modeling of “following-defense” behavior. International Journal of Man-Machine Studies, 8, 597-615.

Furutani, N. 1976b. A new approach to traffic behavior: II. Individual car and traffic flow. International Journal of Man-Machine Studies, 8, 731-742.

Furutani, N. 1977. A new approach to traffic behavior: III. Steering behavior and the butterfly catastrophe. International Journal of Man-Machine Studies, 9, 233-254.

George, D. 1981. Equilibrium and catastrophes. Scottish Journal of Political Economy, 28, 43-61.

Gilmore, R. 1979. Catastrophe time scales and conventions. Physical Review A, 20, 2510-2515.

Gilmore, R. 1981. Catastrophe theory for scientists and engineers. John Wiley & Sons: New York .

Greshov, C., Haveman, H. A., & Oliva, T. A. 1993. Organizational design, inertia and the dynamics of competitive response. Organization Science, 4, 181-208.

Guastello, S. J. 1981. Catastrophe modeling of equity in organizations. Behavioral Science, 26, 63-74.

Guastello, S. J. 1982a. Color matching and shift work: An industrial application of the cusp-difference equation. Behavioral Science, 27, 131-139.

Guastello, S. J. 1982b. Moderator regression and the cusp catastrophe: Application of two-stage personnel selection, training, therapy, and policy evaluation. Behavioral Science, 27, 259-272.

Guastello, S. J. 1984b. Cusp and butterfly catastrophe modeling of two opponent process models: Drug addiction and work performance. Behavioral Science, 29, 258-262.

Guastello, S. J. 1984c. A catastrophe theory evaluation of a policy to control job absence. Behavioral Science, 29, 263-269.

Guastello, S. J. 1985a. Euler buckling in a wheelbarrow obstacle course: A catastrophe with complex lag. Behavioral Science, 30, 204-212.

Guastello, S. J. 1985b. Color matching throughout the work week: An industrial application of the swallowtail-difference equation. Behavioral Science, 30, 213-218.

Guastello, S. J. 1987a. Catastrophe theory: Ten years of progress (Rep. No. 2790). Social and Behavioral Science documents, 17, 4 (42pp).

Guastello, S. J. 1987b. A butterfly catastrophe model of motivations in organizations: Academic performance. Journal of Applied Psychology, 72, 165-182.

Guastello, S. J. 1987c. Catastrophe modeling of the accident process: Risk dispersion for ten industrial classes (Rep. No. 2817). Social and Behavioral Sciences Documents, 17, 41.

Guastello, S. J. 1988a. Catastrophe modeling of the accident process: Organizational subunit size. Psychological Bulletin, 103, 246-255.

Guastello, S. J. 1988b. The organizational security subsystem: Some potentially catastrophic events. Behavioral Science, 33, 48-58.

Guastello, S. J. 1989. Catastrophe modeling of the accident processes: Evaluation of an accident reduction program using the occupational hazards survey. Accid. Anal. Prev., 21, 17-28.

Guastello, S. J. 1991. Psychosocial variables related to transit accidents: A catastrophe model. Work Stress, 5, 17-28.

Guastello, S. J. 1992. Clash of the paradigms: A critique of an examination of the polynomial regression technique for evaluating catastrophe theory hypotheses. Psychological Bulletin, 111, 375-379.

Guastello, S. J. 1992b. Accidents and stress-related health disorders: forecasting with catastrophe theory. In J. Quick, J. J. Hurrell, & L. M. Murphy (Eds.), Work and well-being: Assessments and interventions for occupational mental health (pp.252-269). American Psychological Association: Washington, D.C.

Guastello, S. J. 1995. Chaos, catastrophe, and human affairs: Applications of nonlinear dynamics to work, organizations, and social evolution. Lawrence Erlbaum Associates: Mahwah , New Jersey .

Guastello, S. J. 1998. Self-organization in leadership emergence. Nonlinear Dynamics, Psychology, and Life Sciences, 2, 303-316.

Guastello, S. J. 2000. Nonlinear dynamics in psychology. Discrete Dynamics in Nature and Society, 00, 1-20.

Guastello, S. J. 2002. Managing emergent phenomena: nonlinear dynamics in work organizations. Lawrence Erlbaum Associates: Mahwah , New Jersey .

Guastello, S. J., & Bond, R. W. 2007. A swallowtail catastrophe model for the emergence of leadership in coordination-intensive groups. Nonlinear Dynamics, Psychology, and Life Sciences, 11, 235-251.

Guastello, S. J., Gershon, R. R. M., & Murphy, L. R. 1999. Catastrophe model for the exposure to blood-borne pathogens and other accidents in health care settings. Accident Analysis and Prevention, 31, 739-749.

Guastello, S. J. & McGee, D. W. 1987. Mathematically modeling fatigue in physically demanding jobs. Journal of Mathematical Psychology, 31, 248-269.

Halal, W. E., & Lasken, R. A. 1980. Management applications of catastrophe theory. Business Horizons, 35-42.

Hanges, P. J., Braverman, E. P., & Rentsch, J. R. 1991. Changes in raters' perceptions of subordinates: A catastrophe model. Journal of Applied Psychology, 76, 878-888.

Hardy, L. 1990. A catastrophe model of performance in sport. In J. G. Jones & L. Hardy (Eds.), Stress and performance in sport (pp.81-106). Chichester, UK: Wiley.

Hardy, L. 1993. A test of catastrophe models of anxiety and sports performance against multidimensional anxiety theory models using the method of dynamic differences.

Hardy, L., & Parfitt, C. G. 1991 A catastrophe model of anxiety and performance. British Journal of Psychology, 82, 163-178.

Hardy, L., Parfitt, C. G., & Pates, J. 1995? Performance catastrophes in sport: A test of the hysteresis hypothesis. Journal of Sport Sciences.

Hartelman, P. A. I. 1997. Stochastic catastrophe theory. Dissertatie reeks 1997-2, Faculteit Psychologie, Universiteit van Amsterdam.

Hartelman, P. A. I., van der Maas, H. L. J., Molenaar, P. C. M. 1998. Detecting and modeling developmental transitions. British Journal of Developmental Psychology, 16, 97-122.

Haslett, T., Moss, S., Osborne, C., & Ramm, P. 2000. Local rules and fitness landscapes: A catastrophe model. Nonlinear Dynamics, Psychology, and Life Sciences, 4, 67-86.

Herbig, P. 1991. A cusp catastrophe model of the adoption of an industrial innovation. Journal of Product Innovation Management, 8, 127-137.

Ho, T., & Saunders, A. 1980. A catastrophe model of bank failure. Journal of Finance, 35, 1189-1207.

Holt, R. T., Job, B. L., & Markus, L. 1978. Journal of Conflict Resolution, 22, 171-208.

Horgan, J. 1995. From complexity to perplexity. Scientific American, 272, 104-109.

Horgan, J. 1997. The end of science: Facing the limits of knowledge in the twilight of the scientific age. New York: Broadway Books.

Hufford, M. R. 2001. Alcohol and suicidal behavior. Clinical Psychology Review, 21, 797-811.

Hufford, M. R., Witkiewitz, K., Shields, A. L., Kodya, S., & Caruso, J. C. 2003. Relapse as a nonlinear dynamic system: Application to patients with alcohol use disorder. Journal of Abnormal Psychology, 112, 219-227.

Isnard, C. A., & Zeeman, E. C. 1976. Some models from catastrophe theory in the social sciences. In L. Collins (Ed.), The use of models in the social sciences (pp.44-100). Tavistock: London . [Reprinted in Zeeman, 1977]

Jammemegg, W, & Fischer, E. O. 1986. Economic applications and statistical analysis of the cusp catastrophe model. Zeitschrift Operations Research, 30, B45-B58.

Jiobu, R. M., & Lundgren, T. D. 1978. Catastrophe theory: A quasi-quantitative methodology. Sociological methods & research, 7, 29-54.

Jones, D. D., & Walters, C. J. 1976. Catastrophe theory and fisheries regulation. Journal of the fisheries research board of Canada, 33, 2829-2833.

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Ph.D. Disserations

Many of those who have taken a prominent role in research on catastrophe theory and others who moved on to other things started out with Ph.D. dissertations in the 1970s and early 1980s when the theory was first popularized. There have been a lot of academics who started their work with a dissertation using catastrophe theory. Although I have not made an effort to be comprehensive or to obtain copies and read each of these, I thought I would start noting the references to these in addition to the journal articles, book chapters, and monographs referenced above. One of the advantages to this form of research is that they often give more of the details and better explanations than more short, concise academic articles. As with the previous bibliography, this is not a comprehensive list, but I will continue to add to it as I come across other references.

Abelson, M. A. 1981. Catastrophe theory model of employee withdrawal process leading to job termination. Ph. D. dissertation. The Pennsylvania State University.

Brown, W. S. 1977. An economic application of catastrophe theory. Unpublished doctoral dissertation, University of Colorado, 1977.

Carhart, D. H. 1984. An examination of the potential use of quantified catastrophe theory in management: A case study, or can management tell which straw will break the camel’s back? Ph. D. dissertation The George Washington University.

Guastello, S. J. 1982. Development and validation of a butterfly catastrophe model of academic motivation. Doctoral dissertation, Illinois Institute of Technology.

Hartelman, P. A. I. 1997. Stochastic catastrophe theory. Dissertatie reeks 1997-2, Faculteit Psychologie, Universiteit van Amsterdam. [Also listed previously in the general bibliography]

Johnson, A. F. 1982. An application of catastrophe theory to the structure and operation of a board of directors of a nonprofit organization. Ph. D. dissertation. The Wright Institute (Berkely).

Morrow, J. D. A rational catastrophe theory of war. Ph. D. dissertation. The University of Rochester.

Smith, J. Q. 1981. Problems in Bayesian statistics related to discontinuous phenomena. Catastrophe theory and forecasting. Ph.D. thesis, Warwick University.

Last Modified: 27 Feb 2008