Quantitative Analysis of the Relationship between Three Psychological Parameters Based on Swallowtail Catastrophe Model

A sudden jump in the value of the state variable in a certain dynamical system can be studied through a catastrophe model. This paper presents an application of catastrophe model to solve psychological problems. Since we will have three psychological aspects or parameters, intelligence (I), emotion (E), and adversity (A), a Swallowtail catastrophe model is considered to be an appropriate one. Our methodology consists of three steps: solving the Swallowtail potential function, finding the critical points up to and including threefold degenerates, and fitting the model into our measured data. Using a polynomial curve fitting derived from the potential function of Swallowtail catastrophe model, relations among three parameters combinations are analyzed. Results show that there are catastrophe phenomena for each relation, meaning that a small change in one psychological aspect may cause a dramatic change in another aspect

Theory and application of mathematical science

A sudden jump in the value of the state variable in a certain dynamical system can be studied through a catastrophe model. This paper presents an application of catastrophe model to solve a psychological problems. Since we will have three psychological aspects or parameters. Intelligence (I), Emotion (E), and Adversity (A), a Swallowtail catastrophe model is considered to be an appropriate one. Our methodology consists of three steps : solving the Swallowtail potential function, finding the critical points up to and including three-fold degenerates, and fitting the model into our measured data. Using a polynomial curve fitting derived from the potential function of Swallowtail Catastrophe Model, relations among three parameters combinations are analyzed. Results show that there are catastrophe phenomena for each relations, meaning that a small change in one psychological aspect may cause a dramatically change in another aspec

EAWOP Small Group Meeting 2016 on Non-linear Dynamics in Work and Organizational Psychology: To Non-linear Modelling … and Beyond

EAWOP Small Group Meeting. 17th – 18th October 2016, University of Barcelona, Barcelona, SpainThe main objective of this meeting is to foster debate and knowledge sharing among scholars interested in going beyond the generalized linear modelling. Very often we find, as part of the limitation of empirical researches, statements describing that data could have been also analysed taking advantage of nonlinear methods. However, the application of non-linear models in our field is not as common as it could be.EAWOP / UB / PsicoSAO & Gobierno de España - Ministerio de Economía y Competitividad, project number PSI2013-44854-

"Suddenly I get into the zone": Examining discontinuities and nonlinear changes in flow experiences at work

Work-related flow is defined as a sudden and enjoyable merging of action and awareness that represents a peak experience in the daily lives of workers. Employees" perceptions of challenge and skill and their subjective experiences in terms of enjoyment, interest and absorption were measured using the experience sampling method, yielding a total of 6981 observations from a sample of 60 employees. Linear and nonlinear approaches were applied in order to model both continuous and sudden changes. According to the R2, AICc and BIC indexes, the nonlinear dynamical systems model (i.e. cusp catastrophe model) fit the data better than the linear and logistic regression models. Likewise, the cusp catastrophe model appears to be especially powerful for modelling those cases of high levels of flow. Overall, flow represents a nonequilibrium condition that combines continuous and abrupt changes across time. Research and intervention efforts concerned with this process should focus on the variable of challenge, which, according to our study, appears to play a key role in the abrupt changes observed in work-related flow

Modelling and Forecasting Human Populations using Sigmoid Models

Early this century "S-shaped" curves, sigmoids, gainedpopulari ty among demographers. However, by 1940, the approachhad "fallen out of favour", being criticised for giving po,orresults and having no theoretical validity. It was alsoconsidered that models of total population were of littlepractical interest, the main forecasting procedure currentlyadopted being the bottom-up "cohort-component" method.In the light of poor forecasting performance fromcomponent methods, a re-assessment is given in this thesis of theuse of simple trend models. A suitable means of fitting thesemodels to census data is developed, using a non-linear leastsquares algorithm based on minimisation of a proportionatelyweighted residual sum of squares. It is demonstrated that usefulmodels can be obtained from which, by using a top-downmethodology, component populations and vi tal components can bederived. When these models are recast in a recursiveparameterisation, it is shown that forecasts can be obtainedwhich, it is argued, are superior to existing officialprojections.Regarding theoretical validity, it is argued that sigmoidmodels relate closely to Malthusian theory and give a mathematicalstatement of the demographic transition.In order to judge the sui tabili ty of extrapolating fromsigmoid models, a framework using Catastrophe Theory is developed.It is found that such a framework allows one quali tati vely tomodel population changes resulting from subtle changes ininfluencing variables. The use of Catastrophe Theory hasadvantages over conventional demographic models as it allows amore holistic approach to population modelling