Topological methods in analysis of periodic and chaotic canard-type trajectories

TL;DR

This paper explores how topological methods, including topological degree and a corollary of the Poincare-Bendixson theorem, can be used to analyze complex periodic and chaotic trajectories called canards in dynamical systems.

Contribution

It introduces novel applications of topological degree and Poincare-Bendixson related methods to study multi-dimensional and two-dimensional canard trajectories.

Findings

Topological degree helps analyze multi-dimensional canards.

A Poincare-Bendixson corollary confirms existence of certain periodic canards.

Methods facilitate understanding of chaotic canard trajectories.

Abstract

We investigate the role of topological methods in the analysis of canard-type periodic and chaotic trajectories. In the first part of the paper, we apply topological degree to the analysis of multi-dimensional canards. The second part is devoted to an application of a special corollary of the Poincare-Bendixson theorem to the existence of periodic two-dimensional canards.