On Non-occurrence of Chaos in Non-autonomous Planar Flows

TL;DR

This paper provides a sufficient condition ensuring that non-autonomous planar differential systems do not exhibit chaotic behavior by reducing the systems to scalar equations.

Contribution

It introduces a new criterion for preventing chaos in non-autonomous planar flows through a reduction to scalar differential equations.

Findings

Establishes a sufficient condition for non-chaotic behavior

Reduces complex systems to simpler scalar equations

Provides theoretical insights into chaos prevention

Abstract

By folding nonautonomous differential systems in the plane to scalar differential equations, a sufficient condition for the non-occurrence of chaotic behavior is obtained.