Stochastic nonlinear dynamics of interpersonal and romantic relationships

Small Discoveries Can Have Great Consequences in Love Affairs: The Case of Beauty and the Beast

“…First, a naive model has been studied by Strogatz [1988] in a seminal paper and, then, the analysis has been extended to a series of more general abstract models of romantic relationships [Gragnani et al, 1997;Rinaldi, 1998b;Rinaldi & 36 Gragnani, 1998a,b;Sprott, 2004Sprott, , 2005Rinaldi et al, 2010]. Complex issues involving optimal control theory [Feichtinger et al, 1999;Rey, 2010], time-delays [Liao & Ran, 2007;Son & Park, 2011], fractional-order 38 derivatives [Ahmad & El-Khazali, 2007;Ozalp & Koca, 2012], and time-varying parameters [Sprott, 2005;Wauer et al, 2007;Barley & Cherif, 2011] have also been taken into account as well as love stories involving 40 more than two individuals [Dercole, 1999;Sprott, 2004;Bellomo & Carbonaro, 2006;Ahmad & El-Khazali, 2007;Bellomo & Carbonaro, 2008] However, we must admit that in order to reinforce the analysis and 42 make it more convincing, it is desirable, if not mandatory, to refer to specific and well documented romantic relationships, because the possibility of successfully describing a complex love story with a mathematical 44 model can not be given as granted. In this respect, the existing literature is still quite poor, because only three studies, where love stories are satisfactorily described with mathematical models, are available today.…”

A Modified Fractional Differential Love Model

“…The mathematics to the study of marriage turned into presaged with the aid of Von Bertalanfy [14] and the study has begun to hold both the artistic imaginations and interest of diverse scholars inside the fields of mathematics, physics, sociology, biology, neuroscience, psychology and anthropology [2]. Application of mathematical power to the dynamics of marriage has laid basis for a systematic idea of marital relations [3].…”

Solving ordinary differential equations using genetic algorithms and the Taylor series matrix method

“…Ordinary differential equations rule a wide spectrum of physical phenomena and they constitute the actual basis of our science and technology, being used to describe a plethora of processes, ranging from quantum mechanics [1], heat transfer [2], electrical circuits, optics [3] and all kinds of harmonic oscillations [4], population growth [5] to cosmology dynamics [6] and even to model nonlinear dynamics of interpersonal relationships [7], just to mention a few examples.…”