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

Abstract

Over the last three decades, chaotic dynamics in the field of mathematics, physics, chemistry, engineering, and social science have been studied by many researchers and scholars. In this paper, we reviewed period and chaotic behaviors in fractional-order love model of Romeo and Juliet with Gaussian fuzzy membership function as an external force or external environment. To do this, we fixed parameters a = − 1, b = − 5, c = d = 1 and varied α and β in the fractional-order differential equation of Romeo and Juliet love model, with α and β indicating the magnitude of love status of Romeo and Juliet, respectively. If α and β are the same, the magnitude of love status of Romeo is equal to that of Juliet. If α and β are different, then the magnitude of love status of Romeo is different from that of Juliet. We confirmed that when the difference of fractional order between Romeo and Juliet was small, their love status showed chaotic dynamics. This means that they love each other and the relationship between Romeo and Juliet is mutual and equivalent. When the difference is large, love status showed periodic motion. This means that the relationship between Romeo and Juliet is not equivalent.