Article

A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution

Departamento de Análisis Económico, Universidad Complutense, Madrid, Spain.
PLoS ONE (Impact Factor: 3.23). 03/2010; 5(3):e9881. DOI: 10.1371/journal.pone.0009881
Source: PubMed

ABSTRACT

Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough.
Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics.
These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.

Full-text preview

Available from: PubMed Central
  • Source
    • "All above properties, as well as others, can be well understood by putting them in a rational frame through the use of mathematical models. This is what has been done up to now, starting with a naive model presented in a seminal paper (Strogatz, 1988) and continuing through the analysis of a long series of general and abstract models of romantic relationships (Ahmad & El-Khazali, 2007; Barley & Cherif, 2011; Bielczyk, Bodnar, & Foryś, 2012; Bielczyk, 2013; Buder, 1991; Feichtinger, Jorgensen, & Novak, 1999; Felmlee, 2006; Gragnani, Rinaldi, & Feichtinger, 1997; Liao & Ran, 2007; Ozalp & Koca, 2012; Rey, 2010, 2013; Rinaldi, Della Rossa, & Dercole, 2010; Rinaldi & Gragnani, 1998a, 1998b; Rinaldi, 1998a; Son & Park, 2011; Sprott, 2004, 2005; Wauer, Schwarzer, Cai, & Lin, 2007). However, we must admit that in order to reinforce the analysis and make it more credible, it is desirable, if not mandatory, to refer to specific and well documented love stories, because the possibility of successfully describing a complex romantic relationship with a mathematical model can not be given as granted. "
    [Show abstract] [Hide abstract]
    ABSTRACT: A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.
    Full-text · Article · Apr 2014 · Nonlinear Dynamics Psychology and Life Sciences
  • Source
    • "It defines the unique equilibrium point of (3). As observed in [8], there is an effort gap: the rate of effort at the equilibrium is larger than the rate of least effort c . Note also that the equilibrium values ¯ x and ¯ c = r¯ x are non increasing functions of ρ, because "
    [Show abstract] [Hide abstract]
    ABSTRACT: The lovebirds problem consists in finding the compromise between well–being and efforts that are necessary to sustain a durable sentimental relationship. According to a modeling introduced by J.-M. Rey, the problem can be cast as to find the data for a certain dynamical system, guaranteeing that the associated trajectory belongs to the stable manifold. We further discuss the interpretation by means of the Dynamical Programming Principle and the Hamilton-Jacobi-Bellman framework. It allows us to propose an algorithm to determine numerically the solution of the lovebirds problem.
    Preview · Article · Apr 2014 · Acta Applicandae Mathematicae
  • Source
    • "First, a naive model has 34 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, 2004, 2005; Rinaldi 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. "
    [Show abstract] [Hide abstract]
    ABSTRACT: A mathematical model is proposed for interpreting the love story portrayed by Walt Disney in the film "Beauty and The Beast". The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in specific romantic relationships, but also because it enriches the list of examples in which love stories are satisfactorily described through Ordinary Differential Equations.
    Full-text · Article · Nov 2013 · International Journal of Bifurcation and Chaos
Show more