Solvable nonlinear systems of 2 recursions displaying interesting evolutions

TL;DR

This paper identifies a class of nonlinear two-variable recursive systems whose solutions can be explicitly determined, providing insights into their evolution and potential applications.

Contribution

It introduces a new class of solvable nonlinear systems of two recursions with explicit solutions for arbitrary initial data.

Findings

Explicit solutions for the identified systems are derived.

The systems exhibit interesting and predictable evolution patterns.

The approach simplifies analysis of certain nonlinear recursive models.

Abstract

In this paper a class of simple, but nonlinear, systems of recursions involving $2$ dependent variables $x_{j}\left( n\right) $ is identified, such that the solutions of their initial-values problems -- with arbitrary initial data $x_{j}\left( 0\right) $ -- may be explicitly obtained.