Folding, Cycles and Chaos in Discrete Planar Systems

TL;DR

This paper explores the folding method for discrete planar systems to determine the presence of cycles or chaos, including systems with variable or periodic coefficients, expanding understanding of their dynamic behaviors.

Contribution

It introduces the folding technique to analyze rational difference equations with variable coefficients, providing criteria for cycles and chaos in such systems.

Findings

Identifies conditions for cycles in systems with periodic coefficients

Establishes criteria for chaos in rational difference systems

Analyzes systems converging to autonomous forms

Abstract

We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems that converge to autonomous systems and some that do not; e.g., systems with periodic coefficients.