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

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.

Temporary Bluffing Can Be Rewarding in Social Systems: The Case of Romantic Relationships

“…All properties of model (2), including bifurcations, are thoroughly discussed in Rinaldi and Gragnani [1998a] and Rinaldi et al [2010], where the interested reader can find all mathematical details. Model (2) has also been used in Rinaldi et al [2013] and to show that small discoveries can have great and unexpected consequences in love affairs.…”

Time delays in dyadic interactions on the example of relations between optimists and pessimists

“…Note that Assumptions A1 and A3 together with boundedness of f i correspond to the assumptions posed on the influence functions in Rinaldi and Gragnani 2 where relations between secure individuals are described. Detailed analysis of system (1) can be found in previous studies 1,10,13 thus, below, we only summarize results regarding the existence and stability of steady states. Let (x,̄) represent a steady state, that is, the right-hand side of system (1) is set to zero.…”

“…Further examples of the model application (cf. Rinaldi and Gragnani 2 ) include the analysis of Elisabeth's and Darcy's love from the book “Pride and Prejudice,” 9 the story of the beautiful and the beast from Disney's movie, 10 the story of Cyrano de Bergerac 11 or the love story between Scarlett and Rhett described in “Gone with the Wind.” 12 One should also keep in mind the paper 13 in which the authors consider interactions between different couples classifying high‐ and low‐quality relationships. As can be seen from these examples, one model can be used to describe many situations, and its analysis and interpretation depend on the context.…”

Analysis of Chaotic Behavior in a Novel Extended Love Model Considering Positive and Negative External Environment

“…Rinaldi et al [ 21 , 22 , 23 ] proposed more realistic mathematical models for love affairs than the one proposed by Strogatz and Sprott [ 17 , 18 ]. Their papers were based on love stories from novels, theatre, and movies, like, Pride and Prejudice [ 28 , 29 ], Kathe, Jules and Jim [ 30 ], Scarlett and Rhett [ 31 ], Beauty and The Beast [ 32 ], and Roxanne and Cyrano [ 33 ] and deal with relationships of human love.…”