Dynamical models of love with time-varying fluctuations

Abstract

Human romantic relationships are studied via system dynamics methodology. Starting point is a time-invariant linear model of two individuals without interaction with environment. Specifically, time-dependent fluctuations both in the source terms and the system parameters are introduced and examined in their consequences where also more realistic nonlinear modeling is proposed and analyzed.

Love and Appeal in Standard Couples

“…Some results obtained through simple mathematical models, are already available along this line [Gragnani et al, 1997], [Rinaldi, 1998a,b], [Rinaldi & Gragnani, 1998], [Wauer et al, 2007] but refer only to the case of positive appeals. Here we enlarge the scope of the analysis and deal also with the consequences of negative appeals.…”

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.…”

Chaotic Behavior in Model with a Gaussian Function as External Force

“…We now investigate the chaotic attractor to discover the nature of the chaotic phenomena when we set the parameters as a = −2, b = −2, c = 1, and d = 1 with the Gaussian function f (t) = 5 * Gaussmf (t, (20,50)) as an external force in (3). Figure 7 illustrates the results of the time series and phase portrait with these parameters.…”

“…Several models have been proposed for love: the Romeo and Juliet model [9][10][11][12][13], the Laura and Petrarch model [16,17], the Adam and Eve model [18], and others [19][20][21][22][23][24][25][26]. Among these, the love model based on Romeo and Juliet is most commonly employed in the study of nonlinear dynamics.…”