Side-Comparison for Transition Maps in Multi-Layer Canard Problems

Abstract

The paper deals with multi-layer canard cycles, extending the results of [1]. As a practical tool we introduce the connection diagram of a canard cycle and we show how to determine it in an easy way. This connection diagram presents in a clear way all available information that is necessary to formulate the main system of equations used in the study of the bifurcating limit cycles. In a forthcoming paper we will show that both the type of the layers and the nature of the connections between the layers play an essential role in determining the number and the bifurcations of the limit cycles that can be created from a canard cycle.