Co-Evolution of the General Factor of Personality and the Big Five Factors: A Mathematical Model and Its Application to Methylphenidate

Abstract

This study presents a generalization of a mathematical model, called the “bridge model” in Literature, to study the co-evolution or dynamical relationship between the General Factor of Personality (GFP) and the Big Five Factors (B5F) as a consequence of a stimulus. This generalization permits its application here to study such co-evolution after a dose intake of methylphenidate. On the one hand, a stimulus-response model, an integro-differential equation called the “response model,” predicts the short-term effects of a stimulus on the GFP and on the B5F. The fact that both the GFP and the B5F dynamics can be described by the response model is here referred as the “invariance principle.” On the other hand, the invariance principle leads to the derivation of the bridge model: a second order partial differential equation that relates every B5F to the GFP and time. The outcomes of both experimental designs permit the validation of the response model and of the new bridge model.

Keywords:

• Differential equations
• forecasting
• nonlinear dynamical modeling

Authors contributions

Antonio Caselles: Finding the response model and programming its calibration from the experimental designs data.

Joan C. Micó: Finding the response model and deducing the bridge model from de response model.

Salvador Amigó: Setting up the experimental designs and providing the psychological and biological bases of the General Factor of Personality to find the response model.

Pantaleón D. Romero: Validating qualitatively and quantitatively the response and bridge models from the experimental designs data.