Cusp Catastrophe Model Research Articles

A developmental transition in prehension modeled as a cusp catastrophe

The purpose of the study was to show that the change from reaching without grasping to reaching with grasping during the first 6 months of life carried the characteristics of a discontinuous phase transition (catastrophe). A cross-sectional study was carried out with 58 infants between 60 and 408 days old. The infants were seated in a specially designed seat, and presented with nine detachable balls on a black curved board within reaching distance at shoulder height. The number of reaches without and with grasping were scored from video. A cusp catastrophe model was fitted to the data. A Likelihood-Ratio test indicated that the likelihood of the cusp model was significantly higher, p<.001, than a linear regression model. The cusp model was also compared with a logistic model. Akaike's Information criterion for the cusp catastrophe exceeded the logistic model, thus indicating a general better fit. Based on prior research, the following potential control parameters were chosen: crown–heel length, total body weight, arm length, arm circumference, ponderal index, arm volume, arm weight, and body position relative to the horizontal. The cusp model predicted that arm weight and arm circumference significantly contributed to the control parameters. It was found that these two variables had their largest contribution to the asymmetry control parameters. © 1998 John Wiley & Sons, Inc. Dev Psychobiol 32: 23–35, 1998

A developmental transition in prehension modeled as a cusp catastrophe

The purpose of the study was to show that the change from reaching without grasping to reaching with grasping during the first 6 months of life carried the characteristics of a discontinuous phase transition (catastrophe). A cross-sectional study was carried out with 58 infants between 60 and 408 days old. The infants were seated in a specially designed seat, and presented with nine detachable balls on a black curved board within reaching distance at shoulder height. The number of reaches without and with grasping were scored from video. A cusp catastrophe model was fitted to the data. A Likelihood-Ratio test indicated that the likelihood of the cusp model was significantly higher, p < .001, than a linear regression model. The cusp model was also compared with a logistic model. Akaike's Information criterion for the cusp catastrophe exceeded the logistic model, thus indicating a general better fit. Based on prior research, the following potential control parameters were chosen: crown-heel length, total body weight, arm length, arm circumference, ponderal index, arm volume, arm weight, and body position relative to the horizontal. The cusp model predicted that arm weight and arm circumference significantly contributed to the control parameters. It was found that these two variables had their largest contribution to the asymmetry control parameters.

A cusp catastrophe model for adolescent alcohol use: An empirical test.

The current study was designed to assess the usefulness of a cusp catastrophe model in predicting adolescent alcohol use. The model suggests that dispositions should be viewed as a normal parameter in a cusp catastrophe model and situational pressure serves as a splitting parameter. This conceptualization predicts that as situational pressure increases a bimodal distribution in the underlying behavior should result. Statistical analyses revealed that the cusp model was a better predictor of alcohol use than the alternative linear models. These findings suggest that the modeling of situational pressure variables should be reexamined from within this new framework.

An Investigation of the Zones of Optimal Functioning Hypothesis Within a Multidimensional Framework

Hanin’s (1980) zones of optimal functioning (ZOF) hypothesis suggests that a person is most likely to attain peak performance within an individual, specific bandwidth of state anxiety. The present study investigated Hanin’s ZOF hypothesis within a multidimensional framework, whereby zones of optimal functioning were computed for cognitive and somatic anxiety. Participants (N = 25) were members of a competitive bowling league; they completed the CSAI- 2 prior to each league match over a period of 20 weeks. Performance was operationalized as each participant’s score in the first game of each match, and these scores were standardized within subjects. The analysis revealed a significant main effect for somatic anxiety zone level and a significant interaction between cognitive and somatic anxiety zone levels (below, in, and above zone) and subsequent performance. Results are discussed in terms of the theoretical implications for future researchers, specifically in relation to the cusp catastrophe model.

Catastrophe models and the expansion method: A review of issues and an application to the econometric modeling of economic growth

Many negative reactions to Catastrophe Theory have been triggered by overly simplistic applications unintended and unsuited for statistical‐econometric estimation, inference, and testing. In this paper it is argued that stochastic catastrophe models constructed using the Expansion Method hold the most promise to widen the acceptance of Catastrophe Theory by analytically oriented scholars in the social sciences and elsewhere. The paper presents a typology of catastrophe models, and demonstrates the construction and estimation of an econometric expanded cusp catastrophe model of economic growth.

Sahelian Rangeland Development; A Catastrophe?

This paper sets out that the dynamics of the Sahelian rangeland vegetation can be interpreted as a cusp catastrophe and that this interpretation offers a promising basis for the description and analysis of this ecosystem. Firstly, an existing scheme of the dynamics of Sahelian herbaceous vegetation is translated into the state-and-transition formulation. Secondly, the application of the cusp catastrophe is explored by studying the behaviour of the Sahelian rangeland ecosystem under changing effective rainfall and grazing intensity, using the transitions from the state-and-transition formulation as vectors along the cusp manifold. This conceptual cusp catastrophe model subsequently results in the identification of hypotheses and the detection of 5 catastrophic properties of this ecosystem (bimodality, inaccessibility, sudden jumps, divergence and hysteresis) that have important management implications. The continuous and the discontinuous processes occurring in the Sahelian rangeland ecosystem can both be captured in a unified conceptual model by applying the cusp catastrophe theory. Testing the hypotheses generated by the conceptual model and searching for additional catastrophic properties, such as divergence of linear response and critical slowing down, is a useful direction for future research.

Testing the Predictions of the Cusp Catastrophe Model of Anxiety and Performance

Hardy and Fazey’s (1987) cusp catastrophe model of anxiety and performance has been criticized for being overly complex and difficult to test. The present paper attempts to clarify the model for researchers who are less familiar with its more subtle nuances; it then differentiates between the characteristics of cusp catastrophe models in general and the specific predictions of Hardy and Fazey’s cusp catastrophe model of anxiety and performance. For each prediction, methodological and statistical procedures are suggested whereby the prediction can be tested, and the available evidence that has used these procedures is then briefly reviewed. Some of the practical implications of the cusp catastrophe model for best practice are also discussed.

Nonlinear Analysis

Numerous nonlinear phenomena that exhibit discontinuous jumps in behavior have been modeled with catastrophe theory. Cobb's Cusp Surface Analysis Program (CUSP) provides a way to empirically estimate and test a nonlinear cusp catastrophe model. A model of emotion during problem solving is used to introduce catastrophe theory modeling and is discussed in conjunction with how to run CUSP, how to interpret the output, and how to improve CUSP's performance. Comparisons are made between linear regression and catastrophe theory models and between catastrophe theory gradient dynamics and Cobb's static statistical cusp model.

The relationships among consumer satisfaction, involvement, and product performance: A catastrophe theory application

Attempts to model consumer satisfaction/dissatisfaction (CS/D) responses rely on linear assumptions regarding the effect of various causes (e.g., attribute performance, expectancy discontinuation) on the consumer's reaction to a product or service. This assumption has been pervasive in the CS/D literature despite observations in the trade that consumers are sticky in their preferences or „dispreferences”︁ for products. We present and operationalize a model which relaxes the linearity assumption and allows for lagged and threshold effects of performance increments on CS/D responses in product involvement. Our approach uses the cusp catastrophe model, which has been shown to be robust in a number of contexts, but has had only limited use in the marketing literature. We apply a catastrophe model to data on consumers' use of an appetite suppressant and show that, under high involvement conditions for this product, consumers do not shift preferences over a range of reported performance (e.g., weight loss). The catastrophe model is also shown to be superior to a linear (i.e., OLS) model of the same data.

Mafic enclaves in granitoid intrusions: a catastrophic model of rheological behaviour

The significance of mafic enclaves as indicators of magma mixing processes between juxtaposed felsic and mafic magmas is evaluated from a rheological point of view. A qualitative model for explaining strain and morphological changes in the enclaves has been developed on the basis of the catastrophe theory. Mafic enclaves in intrusive granitoids commonly behave as physical systems that can be described using a cusp catastrophe model. Their behaviour is characterized by bimodality, divergence and sudden changes, which are properties typical of this model. Accordingly, the presence of mafic enclaves showing variable strain and morphology within the same granitoid intrusion would be indicarive of mutual interaction and mingling between mafic and felsic magmas. Due to the characteristics of these processes, it is not possible to establish unambiguous age relationships between the two magmatic components.

Leadership and Information Processing: Linking Perceptions and Performance.

Part 1 Leadership and information processing: introduction information processing and leadership. Part 2 Perceptuals and social processes: recognition-based processes and leadership perceptions inferential processes and leadership perceptions social perception, information processing, and change perceptions of women in management dyadic level leadership and perceptions and reciprocal influence culture, information processing, and leadership. Part 3 Leadership and organizational performance: direct and indirect effects of leadership on performance leadership succession a cusp catastrophe model of organizational performance executive leadership and organizational performance. Part 4 Stability, change and information processing: information processing, change, and executive leadership relations among power, leadership traits, and change conclusions and future research.

Decentralization in growth and decline: A catastrophe theory approach

Catastrophe theory provided a framework to consider the centralization or decentralization of organizational decision-making. The specific concern was the relationship of centralization to the growth or decline in organizational size. Three bodies of literature contributed to the development of hypotheses. First, catastrophe theory suggested a general framework for studying organizational processes. Second, previous theoretical and empirical evidence regarding the relationships between centralization and size suggested the applicability of a cusp catastrophe model. Third, further implications for centralization were drawn from the literature dealing with evolutionary and revolutionary changes in organizational structure. Based on these reviews, catastrophe theory hypotheses were developed concerning the relationship of changes in size to evolutionary and revolutionary changes in the centralization or decentralization of organizational decision-making.

A Catastrophe Theory-Based Model for Quantification of Risk of Low Back Disorders at Work

This paper discusses applications of the catastrophe theory in the dynamic modeling of occupational low back disorders, and offers a framework for conceptualization of such disorders in view of the elementary cusp catastrophe models. It was proposed that low back disorders due to manual lifting should be considered as a discontinuous phenomenon, reflecting dynamic changes in the state of human musculoskeletal system, which are dependent upon the combination of human strength abilities, muscular fatigue and endurance, spinal loading tolerance, as well as dynamic equilibrium between these variables. The behavior of the proposed cusp-catastrophe based model for the risk of LBDs due to manual lifting jobs was examined based on empirical data collected in industry.

Fish and Nutrients Interplay Determines Algal Biomass: A Minimal Model

An analysis is presented of a simple zooplankton-phytoplankton interaction model, accounting for the effects of nutrients and planktivorous fish. The overall behaviour is shown to be analogous to that of the cusp catastrophe model with nutrients and fish as control variables. Predictions that emerge are : gradual change in fish density can lead to discontinuous changes in zooplankton and phytoplankton density under eutrophic conditions; planktivorous fish tends to damp zooplankton-phytoplankton oscillations; enrichment in the absence of fish enhances zooplankton density, but has no effect on algal density, whereas in the presence of a high fish stock the opposite applies. These and other predicted patterns are demonstrated to be present indeed in much field data and experimental results

A Cusp Catastrophe Model of the Adoption of an Industrial Innovation

The diffusion of a technological innovation often follows the pattern of the familiar ‘S’‐curve—the classic smooth, cumulative adoption curve. Yet, an individual firm's decision to adopt or reject an innovation may be filled with discontinuous events, represented by familiar concepts like diffusion thresholds, bandwagon effects and the sudden rejection or displacement of an existing innovation. Paul Herbig reports how catastrophe theory can be used to describe many of these sudden changes and discontinuities. His article describes a model for a firm's adoption or rejection of an innovation via the cusp catastrophe, which he illustrates with a number of possible examples.

A cusp catastrophe model of the adoption of an industrial innovation

The diffusion of a technological innovation often follows the pattern of the familiar ‘S’-curve—the classic smooth, cumulative adoption curve. Yet, an individual firm's decision to adopt or reject an innovation may be filled with discontinuous events, represented by familiar concepts like diffusion thresholds, bandwagon effects and the sudden rejection or displacement of an existing innovation. Paul Herbig reports how catastrophe theory can be used to describe many of these sudden changes and discontinuities. His article describes a model for a firm's adoption or rejection of an innovation via the cusp catastrophe, which he illustrates with a number of possible examples.

COMPUTATIONAL UNFOLDING OF DOUBLE-CUSP MODELS OF OPINION FORMATION

In 1975, Isnard and Zeeman proposed a cusp catastrophe model for the polarization of a social group, such as the population of a democratic nation. Ten years later, Kadyrov combined two of these cusps into a model for the opinion dynamics of two "nonsocialist" nations. This is a nongradient dynamical system, more general than the double-cusp catastrophe studied by Callahan and Sashin [1987]. Here, we present a computational study of the nongradient double cusp, in which the degeneracy of Kadyrov's model is unfolded in codimension eight. Also, we develop a discrete-time cusp model, study the corresponding double cusp, establish its equivalence to the continuous-time double cusp, and discuss some potential applications. We find bifurcations for multiple critical-point attractors, periodic attractors, and (for the discrete case) bifurcations to quasiperiodic and chaotic attractors.

Psychosocial variables related to transit safety: The application of catastrophe theory

Abstract This research applied a paradigm for the study of occupational safety and health risks in manufacturing settings to the risks associated with urban and regional transit operation. Subjects were 290 transit operators who completed a questionnaire measuring safety management, danger ratings, beliefs about accident control, work experience, physical stress, social stress, anxiety, environmental hazards, transit hazards (assaults and insults upon the operator, the need to reprimand passengers for various infractions, etc.), vehicle crashes and operator injuries, and alcohol and drug use. Principal findings were that operator injuries were most closely associated with transit hazards, which were more frequent at night and on the least desirable routes. Injuries occurred in a climate of elevated stress and anxiety which may have hampered the operators' ability to respond effectively to potentially dangerous situations. The cusp catastrophe model provided a non-linear dynamic explanation for accident oc...

Cusp catastrophe model for bulk and broken roof collapse : Pan Yue; Geng Houcai Proc International Symposium on Modern Mining Technology, Taian October 1988 P374–384. Publ Taian: Shandong Institute of Mining and Technology, 1988

Cusp catastrophe model for bulk and broken roof collapse : Pan Yue; Geng Houcai Proc International Symposium on Modern Mining Technology, Taian October 1988 P374–384. Publ Taian: Shandong Institute of Mining and Technology, 1988

A Generic Model of Competitive Dynamics

Using catastrophe theory, this article presents a generic model of competitive dynamics that allows for the integration of structural (industry inertia) and process (relative competitive force) components of competitive dynamics found in the marketplace. More specifically, this article presents a cusp catastrophe model to account for the variety of ways changes in competitive position can occur among competing businesses in an industry, and it builds on the growing body of catastrophe applications to organizational and managerial contexts.