Dynamics of Multidimensional Secession

TL;DR

This paper investigates a generalized Seceder Model with higher-dimensional genotypes and variable group sizes, providing a comprehensive analytical understanding of its stable states and critical behaviors.

Contribution

It introduces a mean-field approach to a multidimensional Seceder Model, identifying critical group sizes and characterizing all stable fixed points analytically.

Findings

Identified the upper critical size for multiplet selection groups.

Mapped the model to a discrete deterministic version.

Provided a complete analytical description of stable fixed points.

Abstract

We explore a generalized Seceder Model with variable size selection groups and higher dimensional genotypes, uncovering its well-defined mean-field limiting behavior. Mapping to a discrete, deterministic version, we pin down the upper critical size of the multiplet selection group, characterize all relevant dynamically stable fixed points, and provide a complete analytical description of its self-similar hierarchy of multiple branch solutions.