Nonlinear Behavior in Romeo and Juliet’s Love Model Influenced by External Force with Fuzzy Membership Function

Abstract

Recently, the study of chaotic behaviors in the social sciences includes the habit and the mind of human can be represented using models which include addiction, happiness, family relationship, and love. Within this field, various forms of love model have widely been studied. One of the most famous love models is the Romeo and Juliet model. To generate chaotic behaviors in the love model of Romeo and Juliet, it is necessary to apply an external force that is organized by a periodic function such as sine or cosine wave, which we assume as an ideal external force. However, because this ideal external force cannot possibly represent the real mind of a human, we need to find a reasonable function that allows us to closely describe the mind of human. In this paper, we propose a function that can describe the mind of human by using fuzzy membership function. To do this, we use Gaussian, sigmoid, and triangular fuzzy membership function as external forces. In order to get nonlinear behaviors by using computer simulation, we fix three parameters (a, c, and d) and vary parameter (b) for love model of Romeo and Juliet with the external forces of Gaussian, sigmoid, and triangular fuzzy membership function. Finally, we find that the external force that represents the nonlinear behaviors in love model of Romeo and Juliet through time series and phase portraits most excellent manner is the triangular fuzzy membership function.