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