Dynamical Galam model

TL;DR

This paper extends the Galam model by making the proportion of inflexibles dynamic, revealing fixed points and phase transitions that influence political opinion evolution, including stable and oscillatory regimes.

Contribution

It introduces a dynamical extension of the Galam model with evolving inflexibles, uncovering new phase behaviors and stability conditions.

Findings

Identification of fixed points controlling opinion dynamics

Discovery of two distinct phases: majority-preserving and regime-changing

Observation of phase transitions between these regimes

Abstract

We introduce a model of temporal evolution of political opinions which amounts to a dynamical extension of Galam model in which the proportions of inflexibles are treated as dynamical variables. We find that the critical value of inflexibles in the original Galam model now turns into a fixed point of the system whose stability controls the phase trajectory of the political opinions. The appearance of two phases, in which majority-preserving and regime-changing limit cycles are respectively dominant, is found, and also the transition between them is observed.