Discrete-Time Dynamical Systems Generated by a Quadratic Operator

TL;DR

This paper studies a class of quadratic operators in discrete-time dynamical systems, identifying fixed points, their stability, and analyzing global dynamics, especially in two dimensions, to extend previous lower-dimensional results.

Contribution

It provides a comprehensive classification of fixed points for a specific quadratic operator class and explores their stability and global dynamics in two dimensions, extending earlier findings.

Findings

No attractive fixed points except the origin.

Fixed points are fully classified and their types identified.

Global dynamics in two dimensions are characterized.

Abstract

In this paper, we examine a specific class of quadratic operators. For these operators, we identified all fixed points and categorized their types in the general case. Our analysis revealed that there are no attractive fixed points except the origin. Additionally, we investigated the global dynamics in the two-dimensional case and generalized several results obtained for lower-dimensional scenarios