Research Article
Quantitative Analysis of the Relationship between
Three Psychological Parameters Based on Swallowtail
Catastrophe Model
Asti Meiza,
1
Sutawanir Darwis,
2
Agus Yodi Gunawan,
3
and Efi Fitriana
4
1
Psychology Faculty, UIN Sunan Gunung Djati-Bandung, Bandung, Indonesia
2
Statistical Research Division of Mathematics and Natural Faculty, Bandung Institute of Technology, Bandung, Indonesia
3
Industrial and Finance Research Division of Mathematics and Natural Faculty, Bandung Institute of Technology, Bandung, Indonesia
4
Faculty of Psychology, Padjadjaran University, Bandung, Indonesia
Correspondence should be addressed to Asti Meiza; asti.meiza@uinsgd.ac.id
Received 8 June 2017; Revised 26 July 2017; Accepted 9 August 2017; Published 26 September 2017
Academic Editor: Niansheng Tang
Copyright © 2017 Asti Meiza et al. Tis is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A sudden jump in the value of the state variable in a certain dynamical system can be studied through a catastrophe model. Tis
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, fnding the critical points up to and
including threefold degenerates, and ftting the model into our measured data. Using a polynomial curve ftting 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.
1. Introduction
A catastrophe phenomenon arising from psychological prob-
lems has frst been discussed by Arnold [1]. In that paper,
he characterized a creative personality of a scientist, as well
as a maniac, by the following three parameters: technical
profciency, enthusiasm, and achievement. He found that
scientist and maniac have diferences in their performance
dramatically. In fact, the achievement of scientist mainly
depended on his technical profciency and enthusiasm. If
enthusiasm was not great, the achievement grew monotoni-
cally and fairly slow with technical profciency. If enthusiasm
was sufciently great then qualitatively dramatic phenomena
start to occur due to a small variation in technical profciency,
while for maniac, he concluded that the latter phenomenon
would not occur. A maniac having similar enthusiasm with
scientist could not change his achievement because their
technical profciencies were diferent. Tis phenomenon was
well modelled by him as Cusp catastrophe model.
Other catastrophe models related to psychological prob-
lems were also studied by [2–6] (Brezeale, 2011). However,
their model was limited to Cusp model. To name a few,
Van der Maas et al. have constructed a deterministic Cusp
catastrophe for “political attitude” as a state variable and
“information” and “involvement” as the two control param-
eters. Cusp was ftted using R routine in the common use
and also used to ft a sudden transition data [7]. Cusp
catastrophe model was also used by [5] to model the
intelligent phenomenon of students (their intelligences and
emotions) when students from various departments were
grouped into one class. Other ftting models based on an
application of estimation theory were worked out by Cobb
[4]. To some extent, catastrophe model was extended to
include more than two control parameters. For instance,
[8] studied relations among three parameters of trafc fow:
velocity, density, and fow, by using a Swallowtail catastrophe
model. Te butterfy catastrophe model for describing and
predicting performance changes in an educational setting
Hindawi
International Journal of Mathematics and Mathematical Sciences
Volume 2017, Article ID 7418132, 6 pages
https://doi.org/10.1155/2017/7418132