Hero's journey in bifurcation diagram

Monteiro L.H.A.; Mustaro P.N.

Hero's journey in bifurcation diagram

Tipo

Artigo

Data de publicação

2012

Periódico

Communications in Nonlinear Science and Numerical Simulation

Citações (Scopus)

4

Autores

Monteiro L.H.A.
Mustaro P.N.

Resumo

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films. © 2011 Elsevier B.V.

Assuntos Scopus

Bifurcation diagram , Chaotic behaviors , Comparative studies , Control parameters , Critical moment , Discrete-time dynamical systems , Fixed points , Gaussian map , Hero's journey , Limit cycle , Narrative structures , Quantitative agreement , Saddle node bifurcation