Rational map associated with the Sigmoid Beverton-Holt model on the projective line over $\mathbb{Q}_p$

TL;DR

This paper analyzes the dynamical behavior of a $p$-adic rational map derived from the Sigmoid Beverton-Holt model, revealing its structure on the projective line over $ extbf{Q}_p$ using minimal polynomial decomposition and chaos theory.

Contribution

It introduces a detailed $p$-adic dynamical analysis of the Sigmoid Beverton-Holt model, employing novel decomposition techniques and chaos descriptions specific to $p$-adic systems.

Findings

Characterization of the $p$-adic dynamical structure

Identification of chaotic behavior in $p$-adic repellers

Application of minimal polynomial decomposition methods

Abstract

We describe the dynamical structure of the $p$-adic rational dynamical systems associated with the Sigmoid Beverton-Holt model on the projective line over the field $\mathbb{Q}_p$ of $p$-adic numbers. Our methods are minimal decomposition of $p$-adic polynomials with coefficients in $\mathbb{Z}_p$ established by Fan and Liao and the chaotic description of $p$-adic repellers of Fan, Liao, Wang and Zhou.