Modified Legendre wavelet-based comparative study of a new model of romantic and interpersonal relationships

Abstract

Current biosocial theories, such as the influence of neurotransmitters on the behaviour, ecological perspectives that consider cultural, political, and institutional factors and interpersonal views like attachment, have shaped our understanding of romantic and interpersonal relationships as typical social experiences. However, these theories fail to offer a comprehensive framework for the relationship dynamics and a fully integrated theoretical approach is still missing. Here, we have developed a mathematical model to investigate the dynamics of romantic and interpersonal relationships between male, female, child and society via a system of fractional differential equations (SFDEs) to provide insight into the love/hate behaviour. The model comprises four classes describing the love/hate of males, females, children and society. The modified operational matrix of integration (OMI) of the Legendre wavelets is presented and used to solve the SFDEs. The model is solved using RK4, NDSolve and the Legendre wavelet collocation method (LWCM) for numerical analysis and comparison of the solutions. Numerical and graphical study of fractional order is done for different values of \(\gamma \). The pictorial analysis of various values of parameters to show the variation of classes is done. The Mathematica software has been used for numerical computations. This study reveals how the internal relationship and status affect the status of the society.