Steady State Classification of Allee Effect System

TL;DR

This paper develops a method to classify steady states in high-dimensional Allee effect systems by reducing the model's complexity and providing an algorithm that handles systems up to seven dimensions.

Contribution

It introduces a reduction technique and an efficient classification algorithm for steady states in high-dimensional Allee effect models, including a comprehensive border polynomial formula.

Findings

Successfully classified steady states for systems up to seven dimensions

Derived a general formula for border polynomial in arbitrary dimensions

Provided an efficient algorithm for parameter classification

Abstract

In this paper, we consider the steady state classification problem of the Allee effect system for multiple tribes. First, we reduce the high-dimensional model into several two-dimensional and three-dimensional algebraic systems such that we can prove a comprehensive formula of the border polynomial for arbitrary dimension. Then, we propose an efficient algorithm for classifying the generic parameters according to the number of steady states, and we successfully complete the computation for up to the seven-dimensional Allee effect system.